77.1.18 problem 34 (page 40)

Internal problem ID [17908]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 34 (page 40)
Date solved : Tuesday, January 28, 2025 at 11:12:07 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=2 y x -x^{3}+x \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

dsolve(diff(y(x),x)=2*x*y(x)-x^3+x,y(x), singsol=all)
 

\[ y = \frac {x^{2}}{2}+{\mathrm e}^{x^{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 21

DSolve[D[y[x],x]==2*x*y[x]-x^3+x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2}{2}+c_1 e^{x^2} \]