60.3.19 problem 1019

Internal problem ID [11029]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1019
Date solved : Monday, January 27, 2025 at 10:42:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ 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: 0.000 (sec). Leaf size: 0

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

Not solved