Internal problem ID [1176]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x -\left (x^{2}-2\right ) y=3 x^{4}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-(x^2-2)*y(x)=3*x^4,y(x), singsol=all)
\[ y \left (x \right ) = \sinh \left (x \right ) x c_{2} +\cosh \left (x \right ) x c_{1} -3 x^{2} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 29
DSolve[x^2*y''[x]-2*x*y'[x]-(x^2-2)*y[x]==3*x^4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x \left (-6 x+2 c_1 e^{-x}+c_2 e^x\right ) \]