Internal problem ID [3845]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 595.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2} y^{\prime }-x \left (1+y^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (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: 0.22 (sec). Leaf size: 39
DSolve[y[x]^2 y'[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*}