Match the Integrating factor of the following Differential equations.
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LIST I |
LIST II |
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A. $\frac{d y}{d x}-y=\cos x$ |
I. $e^x$ |
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B. $\frac{d y}{d x}=\cos x-y$ |
II. $x^2$ |
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C. $x \frac{d y}{d x}+2 y=x^2$ |
III. $\frac{1}{x^2}$ |
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D. $\frac{d y}{d x}=x+\frac{2}{x} y$ |
IV. $e^{-x}$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-IV, B-I, C-II, D-III
(A) $\frac{d y}{d x}-y=\cos x⇒I.F.=e^{-1dx}=e^{-x}$ (IV)
(B) $\frac{dy}{dx}+y=\cos x⇒I.F.=e^{1dx}=e^{x}$ (I)
(C) $\frac{dy}{dx}+\frac{2}{x}y=x⇒I.F.=e^{\frac{2}{x}dx}=e^{\log x^2}=x^2$ (II)
(D) $\frac{dy}{dx}-\frac{2}{x}y=x⇒I.F.=e^{-\frac{2}{x}dx}=e^{\log \frac{1}{x^2}}=\frac{1}{x^2}$ (III)