29.1.8 problem 7

Internal problem ID [4615]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 7
Date solved : Monday, January 27, 2025 at 09:26:20 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=x \left (x^{2}-y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

\[ y \left (x \right ) = x^{2}-2+{\mathrm e}^{-\frac {x^{2}}{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 22

DSolve[D[y[x],x]==x*(x^2-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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