Mark against the correct answer in the following:
Question: Mark $(\sqrt{)}$ against the correct answer in the following: The general solution of the $D E \frac{d y}{d x}=\frac{y}{x}+\sin \frac{y}{x}$ is A. $\tan \frac{\mathrm{y}}{2 \mathrm{x}}=\mathrm{Cx}$ B. $\tan \frac{\mathrm{y}}{\mathrm{x}} \mathrm{Cx}$ C. $\tan \frac{y}{2 x}=C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The general solution of the $\operatorname{DE}(x-y) d y+(x+y) d x$ is A. $\tan ^{-1} \frac{\mathrm{y}}{\mathrm{x}}=\mathrm{C} \sqrt{\mathrm{x}^{2}+\mathrm{y}^{2}}$ B. $\tan ^{-1(y-x)}=C \sqrt{x^{2}+y^{2}}$ C. $\tan ^{-1}\left(\frac{y}{x}\right)=x^{2}+y^{2}+C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The general solution of the DE $2 x y d y+\left(x^{2}-y^{2}\right) d x=0$ is A. $x^{2}+y^{2}=\mathrm{C} x$ B. $x^{2}+y^{2}=C y$ C. $x^{2}+y^{2}=C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The general solution od the DE $x \frac{d y}{d x}=y+x \tan \frac{y}{x}$ is is A. $\sin \left(\frac{y}{x}\right)=C$ B. $\sin \left(\frac{y}{x}\right)=C x$ C. $\sin \left(\frac{\mathrm{y}}{\mathrm{x}}\right)=\mathrm{Cy}$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The general solution of the DE $x^{2} \frac{d y}{d x}=x^{2}+x y+y^{2}$ is. A. $\tan ^{-1} \frac{y}{x}=\log x+C$ B. $\tan ^{-1} \frac{\mathrm{x}}{\mathrm{y}}=\log \mathrm{x}+\mathrm{C}$ C. $\tan ^{-1} \frac{y}{x}=\log y+C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The general solution of the $D E \frac{d y}{d x}=\frac{y^{2}-x^{2}}{2 x y}$ is A. $x^{2}-y^{2}=C_{1} x$ B. $x^{2}+y^{2}=C_{1} y$ C. $x^{2}+y^{2}=C_{1} x$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The general solution of the $D E \frac{d y}{d x}=\left(\sqrt{1-x^{2}}\right)\left(\sqrt{1-y^{2}}\right)$ is A. $\sin ^{-1} y-\sin ^{-1} x=x \sqrt{1-x^{2}}+C$ B. $2 \sin ^{-1} y-\sin ^{-1} x=x \sqrt{1-x^{2}}+C$ C. $2 \sin ^{-1} y-\sin ^{-1} x=C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The general solution of the $D E \log \left(\frac{d y}{d x}\right)=(a x+b y)$ is A. $\frac{-e^{-b y}}{b}=\frac{e^{a x}}{a}+C$ B. $e^{a x}-e^{-b y}=C$ C. $b e^{a x}+a e^{b y}=C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The general solution of the $\operatorname{DEx} \sqrt{1+\mathrm{y}^{2}} \mathrm{dx}+\mathrm{y} \sqrt{1+\mathrm{x}^{2}} \mathrm{dy}=0$ is A. $\sin ^{-1} x+\sin ^{-1} y=C$ B. $\sqrt{1+x^{2}}+\sqrt{1+y^{2}}=C$ C. $\tan ^{-1} x+\tan ^{-1} y=\mathrm{C}$. D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: the general solution of the $D E\left(1+x^{2}\right) d y-x y d x=0$ is A. $y=C\left(1+x^{2}\right)$ B. $y^{2}=C\left(1+x^{2}\right)$ C. $\mathrm{y} \sqrt{1+\mathrm{x}^{2}}=\mathrm{C}$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $D E \frac{d y}{d x}+y \log y \cot x=0$ is A. $\cos x \log y=C$ B. $\sin x \log y=C$ C. $\log y=C \sin x$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: the solution of the DE $x \cos y d y=\left(x \mathrm{e}^{x} \log x+\mathrm{e}^{x}\right) d x$ is A. $\sin y=\mathrm{e}^{x} \log x+C$ B. $\sin y-\mathrm{e}^{x} \log x=\mathrm{C}$ C. $\sin y=\mathrm{e}^{x}(\log x)+C$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $D E \cos x(1+\cos y) d x-\sin y(1+\sin x) d y=0$ is A. $1+\sin x \cos y=\mathrm{C}$ B. $(1+\sin x)(1+\cos y)=\mathrm{C}$ C. $\sin x \cos y+\cos x=\mathrm{C}$ D. none of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $\mathrm{DE} \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{-2 \mathrm{xy}}{\left(\mathrm{x}^{2}+1\right)}$ is A. $y^{2}(x+1)=C$ B. $y\left(x^{2}+1\right)=C$ C. $x^{2}(y+1)=C$ D. None of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: The solution of the $\mathrm{DE} \frac{d y}{d x}=\frac{1-\cos x}{1+\cos x}$ is A. $y=2 \tan \frac{x}{2}-x+C$ B. $y=\tan \frac{x}{2}-2 x+C$ C. $\mathrm{y}=\tan \mathrm{x}-\mathrm{x}+\mathrm{C}$ D. None of these Solution:...
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Question: Mark $(\sqrt{ })$ against the correct answer in the following: The solution of the $D E \frac{d y}{d x}+\sqrt{\frac{1-y^{2}}{1-x^{2}}}=0^{\text {is }}$ A. $y+\sin ^{-1} y=\sin ^{-1} x+C$ B. $\sin ^{-1} y-\sin ^{-1} x=C$ C. $\sin ^{-1} y+\sin ^{-1} x=C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $D E \frac{d y}{d x}=e^{x+y}+x^{2} \cdot e^{y}$ is A. $e^{x-y}+\frac{x^{3}}{3}+C$ B. $e^{x}+e^{-y}+\frac{x^{3}}{3}+C^{\prime}$ C. $e^{x}-e^{-y}+\frac{x^{3}}{3}+C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $\mathrm{DE} \frac{\mathrm{dy}}{\mathrm{dx}}=1-x+y-x y$ is A. $\log (1+y)=x-\frac{x^{2}}{2}+C$ B. $e^{(1+y)}=x-\frac{x^{2}}{2}+C$ C. $\mathrm{e}^{\mathrm{y}}=\mathrm{x}-\frac{\mathrm{x}^{2}}{2}+\mathrm{C}$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $\operatorname{DE} \frac{d y}{d x}=\frac{\left(1+y^{2}\right)}{\left(1+x^{2}\right)}$ is. A. $(y+x)=\mathrm{C}(1-y x)$ B. $(y-x)=\mathrm{C}(1+y x)$ C. $y=(1+x) C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $x \frac{d y}{d x}=\cot y$ is A. $x \cos y=C$ B. $x \tan y=C$ C. $x \sec y=C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $D E x d y+y d x=0$ is A. $x+y=C$ B. $\mathrm{xy}=\mathrm{C}$ c. $\log (x+y)=C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $\operatorname{DE}\left(e^{x}+1\right) y d y=(y+1) e^{x} d x$ is A. $e^{y}=C\left(e^{x}+1\right)(y+1)$ B. $e^{y}=e^{x}+y+1$ C. $y=\left(e^{x}+1\right)(y+1)$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the $D E \frac{d y}{d x}=2^{x+y}$ is A. $2^{\mathrm{x}}+2^{\mathrm{y}}=\mathrm{C}$ B. $2^{\mathrm{x}}+2^{-\mathrm{y}}=\mathrm{C}$ C. $2^{x}-2^{-y}=C$ D. None of these Solution:...
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Question: Mark $(\sqrt{)}$ against the correct answer in the following: The solution of the []DE $\frac{d y}{d x}=e^{x+y}$ is A. $e^{x}+e^{y}=C$ B. $e^{x}-e^{-y}=C$ C. $e^{x}+e^{-y}=C$ D. None of these Solution:...
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Question: Solve $\left(1+\mathrm{y}^{2}\right) \mathrm{dx}+\left(\mathrm{x}-\mathrm{e}^{-\tan ^{-1} \mathrm{y}}\right) \mathrm{dy}=0$, given that when $y=0$, then $x=0$ Solution:...
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