Internal problem ID [3297]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 553.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 \left (x +1\right ) y y^{\prime }+2 x -3 x^{2}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 52
dsolve(2*(1+x)*y(x)*diff(y(x),x)+2*x-3*x^2+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {\left (x +1\right ) \left (x^{3}-x^{2}+c_{1}\right )}}{x +1} \\ y \relax (x ) = -\frac {\sqrt {\left (x +1\right ) \left (x^{3}-x^{2}+c_{1}\right )}}{x +1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.327 (sec). Leaf size: 54
DSolve[2(1+x)y[x] y'[x]+2 x-3 x^2+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {(x-1) x^2+c_1}}{\sqrt {x+1}} \\ y(x)\to \frac {\sqrt {(x-1) x^2+c_1}}{\sqrt {x+1}} \\ \end{align*}