Internal problem ID [1166]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y-2 \sin \relax (x ) x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+3*y(x)=2*x^4*sin(x),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {c_{1} x^{2}}{2}-2 \cos \relax (x )-2 \sin \relax (x ) x +c_{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 25
DSolve[x^2*y''[x]-3*x*y'[x]+3*y[x]==2*x^4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (c_2 x^2-2 x \sin (x)-2 \cos (x)+c_1\right ) \\ \end{align*}