29.21.19 problem 595

Internal problem ID [5189]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 595
Date solved : Monday, January 27, 2025 at 10:18:35 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 22

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

\[ y \left (x \right ) = -\tan \left (\operatorname {RootOf}\left (x^{2}+2 \tan \left (\textit {\_Z} \right )+2 c_{1} -2 \textit {\_Z} \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.255 (sec). Leaf size: 39

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

\begin{align*} y(x)\to \text {InverseFunction}[\text {$\#$1}-\arctan (\text {$\#$1})\&]\left [\frac {x^2}{2}+c_1\right ] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}