Internal problem ID [1043]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {{\mathrm e}^{x} \left (x^{2} y^{2}+2 x y^{2}\right )+6 x +\left (2 x^{2} y \,{\mathrm e}^{x}+2\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 66
dsolve((exp(x)*(x^2*y(x)^2+2*x*y(x)^2)+6*x)+(2*x^2*y(x)*exp(x)+2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-1+\sqrt {-3 \,{\mathrm e}^{x} x^{4}-{\mathrm e}^{x} c_{1} x^{2}+1}\right ) {\mathrm e}^{-x}}{x^{2}} \\ y \relax (x ) = -\frac {\left (1+\sqrt {-3 \,{\mathrm e}^{x} x^{4}-{\mathrm e}^{x} c_{1} x^{2}+1}\right ) {\mathrm e}^{-x}}{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.472 (sec). Leaf size: 74
DSolve[(Exp[x]*(x^2*y[x]^2+2*x*y[x]^2)+6*x)+(2*x^2*y[x]*Exp[x]+2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{-x} \left (1+\sqrt {1+e^x x^2 \left (-3 x^2+c_1\right )}\right )}{x^2} \\ y(x)\to \frac {e^{-x} \left (-1+\sqrt {1+e^x x^2 \left (-3 x^2+c_1\right )}\right )}{x^2} \\ \end{align*}