38.2.17 problem 17

Internal problem ID [6446]
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 : 17
Date solved : Monday, January 27, 2025 at 02:04:20 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 53

dsolve((x-x*y(x)^2)=(x+x^2*y(x))*diff(y(x),x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.130 (sec). Leaf size: 37

DSolve[(x-x*y[x]^2)==(x+x^2*y[x])*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=\frac {\arcsin (y(x))}{\sqrt {1-y(x)^2}}+\frac {c_1}{\sqrt {1-y(x)^2}},y(x)\right ] \]