3.19 problem 1019

Internal problem ID [8599]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1019.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (4 a^{2} b^{2} x^{2} {\mathrm e}^{2 x^{2} b}-1\right ) y=0} \end {gather*}

Solution by Maple

dsolve(diff(diff(y(x),x),x)-(4*a^2*b^2*x^2*exp(2*b*x^2)-1)*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[(1 - 4*a^2*b^2*E^(2*b*x^2)*x^2)*y[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved