Find an explicit particular solution

**DMDil** · July 11th 2009, 12:03 PM

guys i am having hard time starting out with this problem. help me slove this..

Find an explicit particular solution of the initial value problem:
x dy/dx - y = (2x^2)y, y(1) = 1.

**skeeter** · July 11th 2009, 12:32 PM

Originally Posted by DMDil

guys i am having hard time starting out with this problem. help me slove this..

Find an explicit particular solution of the initial value problem:
x dy/dx - y = (2x^2)y, y(1) = 1.

$x \cdot \frac{dy}{dx} - y = 2x^2y$

$x \cdot \frac{dy}{dx} = 2x^2y + y$

$x \cdot \frac{dy}{dx} = y(2x^2 + 1)$

$\frac{dy}{y} = \left(2x + \frac{1}{x}\right) \, dx$

finish up

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