Internal problem ID [4583]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y+1\right ) x^{2}+y^{2} \left (x -1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 30
dsolve(x^2*(y(x)+1)+y(x)^2*(x-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {x^{2}}{2}+x +\ln \left (x -1\right )+\frac {y \relax (x )^{2}}{2}-y \relax (x )+\ln \left (y \relax (x )+1\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.417 (sec). Leaf size: 54
DSolve[x^2*(y[x]+1)+y[x]^2*(x-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{2} (\text {$\#$1}+1)^2-2 (\text {$\#$1}+1)+\log (\text {$\#$1}+1)\&\right ]\left [-\frac {1}{2} x (x+2)-\log (x-1)+\frac {3}{2}+c_1\right ] \\ y(x)\to -1 \\ \end{align*}