Internal problem ID [11602]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises
page 37
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\frac {x}{y^{2}}+\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 52
dsolve((x/y(x)^2+x)+(x^2/y(x)^3+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {\left (-2 y \left (x \right )^{2}-2\right ) \ln \left (y \left (x \right )^{2}+1\right )+y \left (x \right )^{4}+\left (x^{2}+2 c_{1} +1\right ) y \left (x \right )^{2}+2 c_{1} -1}{2 y \left (x \right )^{2}+2} = 0 \]
✓ Solution by Mathematica
Time used: 0.4 (sec). Leaf size: 55
DSolve[(x/y[x]^2+x)+(x^2/y[x]^3+y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {x^2 y(x)^2}{2 \left (y(x)^2+1\right )}+\frac {y(x)^2}{2}-\frac {1}{2 \left (y(x)^2+1\right )}-\log \left (y(x)^2+1\right )=c_1,y(x)\right ] \]