Internal problem ID [3336]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 594.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{2} y^{\prime }+x \left (-y+2\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(y(x)^2*diff(y(x),x)+x*(2-y(x)) = 0,y(x), singsol=all)
\[ \frac {x^{2}}{2}-\frac {y \relax (x )^{2}}{2}-2 y \relax (x )-4 \ln \left (y \relax (x )-2\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.297 (sec). Leaf size: 43
DSolve[y[x]^2 y'[x]+x(2-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1}^2}{2}+2 \text {$\#$1}+4 \log (\text {$\#$1}-2)-6\&\right ]\left [\frac {x^2}{2}+c_1\right ] \\ y(x)\to 2 \\ \end{align*}