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]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (x^{2}+6\right ) y=x^{4}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
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)
\[ y \left (x \right ) = x^{2} \left (1+\sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 38
DSolve[x^2*y''[x]-4*x*y'[x]+(x^2+6)*y[x]==x^4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x^2 \left (2 c_1 e^{-i x}-i c_2 e^{i x}+2\right ) \]