Internal problem ID [3805]
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]
\[ \boxed {2 \left (x +1\right ) y y^{\prime }+y^{2}=3 x^{2}-2 x} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \frac {\sqrt {\left (x +1\right ) \left (x^{3}-x^{2}+c_{1} \right )}}{x +1} y \left (x \right ) = -\frac {\sqrt {\left (x +1\right ) \left (x^{3}-x^{2}+c_{1} \right )}}{x +1} \end{align*}
✓ Solution by Mathematica
Time used: 0.363 (sec). Leaf size: 56
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^3-x^2+c_1}}{\sqrt {x+1}} y(x)\to \frac {\sqrt {x^3-x^2+c_1}}{\sqrt {x+1}} \end{align*}