77.1.133 problem 160 (page 236)

Internal problem ID [18023]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 160 (page 236)
Date solved : Tuesday, January 28, 2025 at 11:20:43 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-2*y(x)=4*x^2*exp(x^2),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: 0.252 (sec). Leaf size: 36

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

\[ y(x)\to e^{x^2}+c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x} \]