29.10.21 problem 287

Internal problem ID [4887]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 287
Date solved : Monday, January 27, 2025 at 09:46:30 AM
CAS classification : [_linear]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=x \left (3 x^{2}-y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

dsolve((x^2+1)*diff(y(x),x) = x*(3*x^2-y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 22

DSolve[(1+x^2)*D[y[x],x]==x*(3*x^2-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+\frac {c_1}{\sqrt {x^2+1}}-2 \]