Internal problem ID [6715]
Book: Second order enumerated odes
Section: section 2
Problem number: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y+3 \,{\mathrm e}^{x^{2}} \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 35
dsolve(diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2-1)*y(x)=-3*exp(x^2)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x^{2}} \cos \relax (x ) c_{2}+{\mathrm e}^{x^{2}} \sin \relax (x ) c_{1}-\frac {3 \,{\mathrm e}^{x^{2}} \left (-x \cos \relax (x )+\sin \relax (x )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 47
DSolve[y''[x]-4*x*y'[x]+(4*x^2-1)*y[x]==-3*Exp[x^2]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{x^2} ((6 x+4 c_1-2 i c_2) \cos (x)+(-3-4 i c_1+2 c_2) \sin (x)) \\ \end{align*}