Internal problem ID [3406]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 667.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2} \left (a +y\right )^{2} y^{\prime }-\left (x^{2}+1\right ) \left (y^{2}+a^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 92
dsolve(x^2*(a+y(x))^2*diff(y(x),x) = (x^2+1)*(y(x)^2+a^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {-a \RootOf \left (\textit {\_Z}^{2} a^{2} x^{2}-2 c_{1} \textit {\_Z} a \,x^{2}-2 \textit {\_Z} a \,x^{3}+x^{2} c_{1}^{2}+2 x^{3} c_{1}+a^{2} x^{2}+x^{4}-x^{2} {\mathrm e}^{\textit {\_Z}}+2 a \textit {\_Z} x -2 c_{1} x -2 x^{2}+1\right ) x +c_{1} x +x^{2}-1}{x} \]
✓ Solution by Mathematica
Time used: 0.487 (sec). Leaf size: 48
DSolve[x^2 (a+y[x])^2 y'[x]==(1+x^2)(a^2+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [a \log \left (\text {$\#$1}^2+a^2\right )+\text {$\#$1}\&\right ]\left [x-\frac {1}{x}+c_1\right ] \\ y(x)\to -i a \\ y(x)\to i a \\ \end{align*}