Internal problem ID [8631]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1051.
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: 0.004 (sec). Leaf size: 27
dsolve(diff(diff(y(x),x),x)-4*x*diff(y(x),x)+(4*x^2-3)*y(x)-exp(x^2)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x \left (x +1\right )} c_{2}+{\mathrm e}^{x \left (x -1\right )} c_{1}-{\mathrm e}^{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 33
DSolve[-E^x^2 + (-3 + 4*x^2)*y[x] - 4*x*y'[x] + y''[x] == 0,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*}