Internal problem ID [7471]
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]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-1\right ) y=-3 \,{\mathrm e}^{x^{2}} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = {\mathrm e}^{x^{2}} \cos \left (x \right ) c_{2} +{\mathrm e}^{x^{2}} \sin \left (x \right ) c_{1} -\frac {3 \,{\mathrm e}^{x^{2}} \left (-\cos \left (x \right ) x +\sin \left (x \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 50
DSolve[y''[x]-4*x*y'[x]+(4*x^2-1)*y[x]==-3*Exp[x^2]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} e^{x (x-i)} \left (6 x+e^{2 i x} (6 x+3 i-4 i c_2)-3 i+8 c_1\right ) \]