Internal problem ID [1070]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page
91
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {y^{2}+\left (x y^{2}+6 y x +\frac {1}{y}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 39
dsolve((y(x)^2)+(x*y(x)^2+3*x*y(x)+3*x*y(x)+1/y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ x -\frac {3}{y \relax (x )^{4}}+\frac {1}{y \relax (x )^{3}}+\frac {6}{y \relax (x )^{5}}-\frac {6}{y \relax (x )^{6}}-\frac {{\mathrm e}^{-y \relax (x )} c_{1}}{y \relax (x )^{6}} = 0 \]
✓ Solution by Mathematica
Time used: 0.201 (sec). Leaf size: 41
DSolve[(y[x]^2)+(x*y[x]^2+3*x*y[x]+3*x*y[x]+1/y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=-\frac {y(x)^3-3 y(x)^2+6 y(x)-6}{y(x)^6}+\frac {c_1 e^{-y(x)}}{y(x)^6},y(x)\right ] \]