Internal problem ID [1060]
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: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{\prime }+2 y x +\frac {{\mathrm e}^{-x^{2}} \left (3 x +2 y \,{\mathrm e}^{x^{2}}\right )}{2 x +3 y \,{\mathrm e}^{x^{2}}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 36
dsolve([diff(y(x),x)+2*x*y(x)= -exp(-x^2)*(3*x+2*y(x)*exp(x^2))/(2*x+3*y(x)*exp(x^2)),y(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (2 x \,{\mathrm e}^{x^{2}}+\sqrt {\left (-5 x^{2}+9\right ) {\mathrm e}^{2 x^{2}}}\right ) {\mathrm e}^{-2 x^{2}}}{3} \]
✓ Solution by Mathematica
Time used: 33.204 (sec). Leaf size: 44
DSolve[{y'[x]+2*x*y[x]== -Exp[-x^2]*(3*x+2*y[x]*Exp[x^2])/(2*x+3*y[x]*Exp[x^2]),y[0]==-1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3} e^{-2 x^2} \left (2 e^{x^2} x+\sqrt {e^{2 x^2} \left (9-5 x^2\right )}\right ) \\ \end{align*}