Internal problem ID [2496]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{2}+x -1+\left (2 y x +y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 55
dsolve((x^2+x-1)+(2*x*y(x)+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-2 x^{2}+5 \ln \left (1+2 x \right )+4 c_{1}-2 x}}{2} \\ y \relax (x ) = \frac {\sqrt {-2 x^{2}+5 \ln \left (1+2 x \right )+4 c_{1}-2 x}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 69
DSolve[(x^2+x-1)+(2*x*y[x]+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \sqrt {-2 x (x+1)+5 \log (2 x+1)-\frac {1}{2}+8 c_1} \\ y(x)\to \frac {1}{2} \sqrt {-2 x (x+1)+5 \log (2 x+1)-\frac {1}{2}+8 c_1} \\ \end{align*}