Internal problem ID [3384]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 645.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (y+a \right )^{2} y^{\prime }-b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 33
dsolve(x*(a+y(x))^2*diff(y(x),x) = b*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (\ln \relax (x ) {\mathrm e}^{\textit {\_Z}} b +c_{1} b \,{\mathrm e}^{\textit {\_Z}}-2 \textit {\_Z} a \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}}+a^{2}\right )} \]
✓ Solution by Mathematica
Time used: 0.392 (sec). Leaf size: 37
DSolve[x(a+y[x])^2 y'[x]==b y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [-\frac {a^2}{\text {$\#$1}}+2 a \log (\text {$\#$1})+\text {$\#$1}\&\right ][b \log (x)+c_1] \\ y(x)\to 0 \\ \end{align*}