Internal problem ID [5103]
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`]]
\[ \boxed {-x y^{2}-\left (x +y x^{2}\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve((x-x*y(x)^2)=(x+x^2*y(x))*diff(y(x),x),y(x), singsol=all)
\[ x +\frac {\sqrt {y \left (x \right )^{2}-1}\, \ln \left (y \left (x \right )+\sqrt {y \left (x \right )^{2}-1}\right )}{\left (y \left (x \right )-1\right ) \left (y \left (x \right )+1\right )}-\frac {c_{1}}{\sqrt {y \left (x \right )-1}\, \sqrt {y \left (x \right )+1}} = 0 \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 55
DSolve[(x-x*y[x]^2)==(x+x^2*y[x])*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=-\frac {2 \arctan \left (\frac {\sqrt {1-y(x)^2}}{y(x)+1}\right )}{\sqrt {1-y(x)^2}}+\frac {c_1}{\sqrt {1-y(x)^2}},y(x)\right ] \]