Question

If the solution of the differential equation \(x \frac{d y}{d x}+y=x e^{x}\) be, \(x y=e^{x} \varphi(x)+c\) then \(\varphi(x)\) is equal to
(A) \(x+1\)
(B) \(x-1\)
(C) \(1-x\)
(D) \(x\)

Answer 1

Ans: (B)
 If \(=e^{\int \frac{d x}{x}}=e^{\ell \ln x}=x\)
$$
\therefore x y=\int x e^{x} d x=(x-1) e^{x}+c
$$

Answer 2

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Answer 3

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