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]]
\[ \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y=2 \sin \left (x \right ) x^{4}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
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)
\[ y \left (x \right ) = \frac {\left (c_{1} x^{2}-4 x \sin \left (x \right )-4 \cos \left (x \right )+2 c_{2} \right ) x}{2} \]
✓ Solution by Mathematica
Time used: 0.05 (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]
\[ y(x)\to x \left (c_2 x^2-2 x \sin (x)-2 \cos (x)+c_1\right ) \]