Second order non homogeneous differential equation

**lso** · February 10th 2011, 01:45 AM

I have to solve this DE
((x+2)^2)y'' -2y=4

the hint says to get rid of the x+2 but I have no idea where to start from... do I have to replace x+2 with another variable or what?

**Ackbeet** · February 10th 2011, 02:21 AM

I would replace the $x+2$ with $t=x+2,$ and you get

$\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=\dfrac {dy}{dx}.$ Hence, the DE becomes

$t^{2}\,\dfrac{d^{2}y}{dt^{2}}-2y=4.$

This equation is a Cauchy-Euler equation.

Thread: Second order non homogeneous differential equation

LinkBack

Thread Tools

Display

Second order non homogeneous differential equation

Similar Math Help Forum Discussions

First Order Differential Equation (Homogeneous?)

Homogeneous 1st order Differential Equation

2nd order homogeneous differential equations with constant coeficients

second order differential constant coefficients homogeneous

Second order homogeneous equation

Search Tags