60.3.7 problem 1007

Internal problem ID [11017]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1007
Date solved : Monday, January 27, 2025 at 10:41:50 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 26

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

\[ y = {\mathrm e}^{\sqrt {2}\, x} c_{2} +{\mathrm e}^{-\sqrt {2}\, x} c_{1} +{\mathrm e}^{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.286 (sec). Leaf size: 106

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

\[ y(x)\to e^{-\sqrt {2} x} \left (e^{2 \sqrt {2} x} \int _1^x\sqrt {2} e^{K[1] \left (K[1]-\sqrt {2}\right )} K[1]^2dK[1]+\int _1^x-\sqrt {2} e^{K[2] \left (K[2]+\sqrt {2}\right )} K[2]^2dK[2]+c_1 e^{2 \sqrt {2} x}+c_2\right ) \]