y=var('y')
y=function('y',x)
dy=diff(y,x,4)-2*diff(y,x,2)+y==0
desolve_laplace(dy,y,x)

sol:
1/4*x*e^(-x)*y(0) - 1/4*x*e^(-x)*D[0](y)(0) - 1/4*x*e^(-x)*D[0, 0](y)(0)
+ 1/4*x*e^(-x)*D[0, 0, 0](y)(0) - 1/4*x*e^x*y(0) - 1/4*x*e^x*D[0](y)(0)
+ 1/4*x*e^x*D[0, 0](y)(0) + 1/4*x*e^x*D[0, 0, 0](y)(0) + 1/4*(2*y(0) -
3*D[0](y)(0) + D[0, 0, 0](y)(0))*e^(-x) + 1/4*(2*y(0) + 3*D[0](y)(0) -
D[0, 0, 0](y)(0))*e^x

code_ends

    *

      Solution by:

Kreyszig-2-14_34 (last edited 2010-12-18 08:10:05 by anvesh)