differential equation

**hmmmm** · January 14th 2009, 09:46 AM

can anyone help me with this
Find the general solution of x.dy/dx-y=x^2.e^x
thanks for any help

**Danny** · January 14th 2009, 10:16 AM

Originally Posted by hmmmm

can anyone help me with this
Find the general solution of x.dy/dx-y=x^2.e^x
thanks for any help

Put in standard form

$(1)\;\;\;\frac{dy}{dx} - \frac{y}{x} = x e^x$

The integrating factor is $\mu = exp(\int -\frac{1}{x}\,dx) = \frac{1}{x}$ . Multiplying (1) by this gives

$\frac{1}{x} \left( \frac{dy}{dx} - \frac{y}{x} \right) = \frac{d}{dx} \left( \frac{1}{x} \cdot y \right) = e^x$

If you let $u = \frac{y}{x}$ your equation will separate.

Thread: differential equation

LinkBack

Thread Tools

Display

differential equation

Similar Math Help Forum Discussions

[SOLVED] Partial Differential Equation satisfy corresponding equation

Transforming a differential equation into another differential equation

problem on matrix ricaati equation for nonlinear singular differential equation

Partial differential equation-wave equation(2)

Partial differential equation-wave equation - dimensional analysis

Search Tags