Internal problem ID [2020]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+6\right ) y-{\mathrm e}^{-x^{2}} \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+4*x*diff(y(x),x)+(4*x^2+6)*y(x)=exp(-x^2)*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-x^{2}} \cos \left (2 x \right ) c_{2}+{\mathrm e}^{-x^{2}} \sin \left (2 x \right ) c_{1}-\frac {x \,{\mathrm e}^{-x^{2}} \cos \left (2 x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 52
DSolve[y''[x]+4*x*y'[x]+(4*x^2+6)*y[x]==Exp[-x^2]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{32} e^{-x (x+2 i)} \left (-4 x-e^{4 i x} (4 x+i+8 i c_2)+i+32 c_1\right ) \\ \end{align*}