Internal problem ID [1181]
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: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y-x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(x^2+6)*y(x)=x^4,y(x), singsol=all)
\[ y \relax (x ) = x^{2} \sin \relax (x ) c_{2}+x^{2} \cos \relax (x ) c_{1}+x^{2} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 37
DSolve[x^2*y''[x]-4*x*y'[x]+(x^2+6)*y[x]==x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x^2 \left (2 c_1 e^{-i x}+c_2 (\sin (x)-i \cos (x))+2\right ) \\ \end{align*}