Internal problem ID [1026]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 51.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(y)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (y+{\mathrm e}^{x^{2}}\right ) y^{\prime }-2 x \left (y^{2}+y \,{\mathrm e}^{x^{2}}+{\mathrm e}^{2 x^{2}}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve((y(x)+exp(x^2))*diff(y(x),x)=2*x*(y(x)^2+y(x)*exp(x^2)+exp(2*x^2)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-1-\sqrt {2 x^{2}-2 c_{1}+1}\right ) {\mathrm e}^{x^{2}} \\ y \relax (x ) = \left (-1+\sqrt {2 x^{2}-2 c_{1}+1}\right ) {\mathrm e}^{x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.786 (sec). Leaf size: 76
DSolve[(y[x]+Exp[x^2])*y'[x]==2*x*(y[x]^2+y[x]*Exp[x^2]+Exp[2*x^2]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{x^2}-\frac {\sqrt {2 x^2+1+c_1}}{\sqrt {e^{-2 x^2}}} \\ y(x)\to -e^{x^2}+\frac {\sqrt {2 x^2+1+c_1}}{\sqrt {e^{-2 x^2}}} \\ \end{align*}