Internal problem ID [4595]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]], [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x -y^{2} x -\left (x +x^{2} y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 56
dsolve((x-x*y(x)^2)=(x+x^2*y(x))*diff(y(x),x),y(x), singsol=all)
\[ x +\frac {\sqrt {\left (y \relax (x )-1\right ) \left (y \relax (x )+1\right )}\, \ln \left (y \relax (x )+\sqrt {-1+y \relax (x )^{2}}\right )}{\left (y \relax (x )-1\right ) \left (y \relax (x )+1\right )}-\frac {c_{1}}{\sqrt {y \relax (x )-1}\, \sqrt {y \relax (x )+1}} = 0 \]
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 37
DSolve[(x-x*y[x]^2)==(x+x^2*y[x])*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {\text {ArcSin}(y(x))}{\sqrt {1-y(x)^2}}+\frac {c_1}{\sqrt {1-y(x)^2}},y(x)\right ] \]