# Euler's equation

• Aug 30th 2010, 03:55 AM
Euler's equation
the differential equation I have is X^2y'' - 3xy' + 4y = x^2

Ive used Euler's equation to reduce it to y'' - 4y' + 4y = x^2

To solve this I know i need yc + yp and I have worked out Yc to equal (A + bx)e^2x

But its the yp im more worried about... with the x^2 do i have to let x = e^z?

if i do then I should get e^2x? then the guess i would make for yp would be Ae^2x? but so i need to do this? when i changed it to e^2x it cancelled out...so i tried Axe^2x and it cancelled out again -.-"" what do i do now??
• Aug 30th 2010, 05:01 AM
mr fantastic
Quote:

the differential equation I have is X^2y'' - 3xy' + 4y = x^2

Ive used Euler's equation to reduce it to y'' - 4y' + 4y = x^2

To solve this I know i need yc + yp and I have worked out Yc to equal (A + bx)e^2x

But its the yp im more worried about... with the x^2 do i have to let x = e^z?

if i do then I should get e^2x? then the guess i would make for yp would be Ae^2x? but so i need to do this? when i changed it to e^2x it cancelled out...so i tried Axe^2x and it cancelled out again -.-"" what do i do now??

To find the particular solution, use the method of undetermined coefficients: yp = ax^2 + bx + c and your job is to get the values of a, b and c.
• Aug 30th 2010, 05:03 AM