38.2.5 problem 5

Internal problem ID [6434]
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
Date solved : Monday, January 27, 2025 at 02:02:57 PM
CAS classification : [_separable]

\begin{align*} x^{2} \left (y+1\right )+y^{2} \left (x -1\right ) y^{\prime }&=0 \end{align*}

✓ 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)
 

\[ \frac {x^{2}}{2}+x +\ln \left (x -1\right )+\frac {y^{2}}{2}-y+\ln \left (y+1\right )+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.463 (sec). Leaf size: 56

DSolve[x^2*(y[x]+1)+y[x]^2*(x-1)*D[y[x],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 {x^2}{2}-x-\log (x-1)+\frac {3}{2}+c_1\right ] \\ y(x)\to -1 \\ \end{align*}