Internal problem ID [6717]
Book: Second order enumerated odes
Section: section 2
Problem number: 32.
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}-3\right ) y-{\mathrm e}^{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2-3)*y(x)=exp(x^2),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\left (x +1\right ) x} c_{2}+{\mathrm e}^{\left (x -1\right ) x} c_{1}-{\mathrm e}^{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 33
DSolve[y''[x]-4*x*y'[x]+(4*x^2-3)*y[x]==Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{(x-1) x} \left (e^x \left (-2+c_2 e^x\right )+2 c_1\right ) \\ \end{align*}