Solveeit Logo
Login

Question

Question: Solution of the differential equation \(\frac{dy}{dx}\) + \(\frac{y}{x}\) = x<sup>2</sup> under the ...

Solution of the differential equation dydx\frac{dy}{dx} + yx\frac{y}{x} = x2 under the condition that y = 1 when x = 1, is

A

4xy = x3 + 3

B

4xy = x4 + 3

C

4xy = x2 + 3

D

4xy = y3 + 3

Answer

4xy = x4 + 3

Explanation

Solution

Given equation is linear

P = 1/x, q = x2

Solution is y(x) = ∫(x2)xdx\int_{}^{}{(x^{2})xdx}

xy = x44\frac{x^{4}}{4}+ C …(1)

I.F. = e∫1xdx=elnxe^{\int_{}^{}{\frac{1}{x}dx}} = e^{\mathcal{l}nx} = x

Passes through (1, 1)

1 = 1/4 + C ̃ C = 3/4

put C in (1)