Match List – I with List – II.
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LIST I |
LIST II |
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A. $\frac{d y}{d x}=e^{x-y}+x^2 e^{-y}$ |
I. Linear Differential Equation of type $\frac{d y}{d x}+P y=Q$ |
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B. $\frac{d y}{d x}-2 y=\cos 3 x$ |
II. Homogeneous Differential Equation |
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C. $x^2 \frac{d y}{d x}=x^2-2 y^2+x y$ |
III. Linear Differential Equation of type $\frac{d y}{d x}+P x=Q$ |
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D. $\left(x+2 y^3\right) \frac{d y}{d x}=y$ |
IV. Variable separable |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) - A-IV, B-I, C-II, D-III
(A) $\frac{d y}{d x}=e^{x-y}+x^2 e^{-y}⇒\frac{d y}{d x}=\frac{e^x+x^2}{e^y}$
so $\int e^ydy=\int e^x+x^2dx$ (IV)
(B) $\frac{d y}{d x}-2 y=\cos 3 x$ (I)
(C) $x^2 \frac{d y}{d x}=x^2-2 y^2+x y⇒\frac{d y}{d x}=1-2(\frac{y}{x})^2+(\frac{y}{x})=f(\frac{y}{x})$ (II)
(D) $\left(x+2 y^3\right) \frac{d y}{d x}=y$
so $\frac{dx}{dy}-\frac{x}{y}=2y^2$ (III)