Internal problem ID [1171]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y-x^{3} \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+(x^2+2)*y(x)=x^3*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) x c_{2} +\cos \left (x \right ) x c_{1} +\frac {\sin \left (x \right ) x^{2}}{2} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 40
DSolve[x^2*y''[x]-2*x*y'[x]+(x^2+2)*y[x]==x^3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x ((1+4 c_1-2 i c_2) \cos (x)+2 (x-2 i c_1+c_2) \sin (x)) \\ \end{align*}