21.19 problem 595

Internal problem ID [3337]

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]

Solve \begin {gather*} \boxed {y^{2} y^{\prime }-x \left (1+y^{2}\right )=0} \end {gather*}

Solution by Maple

Time used: 0.032 (sec). Leaf size: 22

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

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

Solution by Mathematica

Time used: 0.206 (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 {$\#$1}-\text {ArcTan}(\text {$\#$1})\&]\left [\frac {x^2}{2}+c_1\right ] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}