Solution of $\frac{d y}{d x}+\frac{y}{x}

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

Solution of $\frac{d y}{d x}+\frac{y}{x}=x^2$ is :

Options:

$x+y=\frac{x^2}{2}+c$

$x-y=\frac{x^3}{3}+c$

$x y=\frac{1}{4} x^4+c$

$y-x=\frac{1}{4} x^4+c$

Correct Answer:

$x y=\frac{1}{4} x^4+c$

Explanation:

$\frac{d y}{d x}+\frac{y}{x}=x^2$

I.F. = $e^{\int \frac{d x}{x}}=x$

Therefore solution is $xy=\int x^2 . x d x=\frac{x^4}{4}+c$

Hence (3) is the correct answer.