Internal problem ID [8705]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1125.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 y x^{3}-4 x^{5}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(x*diff(diff(y(x),x),x)+(4*x^2-1)*diff(y(x),x)-4*x^3*y(x)-4*x^5=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x^{2} \left (\sqrt {2}-1\right )} c_{2}+{\mathrm e}^{-x^{2} \left (1+\sqrt {2}\right )} c_{1}-x^{2}-2 \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 45
DSolve[-4*x^5 - 4*x^3*y[x] + (-1 + 4*x^2)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^2+e^{-\left (\left (1+\sqrt {2}\right ) x^2\right )} \left (c_1 e^{2 \sqrt {2} x^2}+c_2\right )-2 \\ \end{align*}