12.6.31 problem 40

Internal problem ID [1710]
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
Date solved : Monday, January 27, 2025 at 05:31:24 AM
CAS classification : [[_Abel, `2nd type`, `class B`]]

\begin{align*} 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}}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.161 (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)
 

\[ y = -\frac {\left (2 x \,{\mathrm e}^{x^{2}}+\sqrt {{\mathrm e}^{2 x^{2}} \left (-5 x^{2}+9\right )}\right ) {\mathrm e}^{-2 x^{2}}}{3} \]

✓ Solution by Mathematica

Time used: 33.120 (sec). Leaf size: 44

DSolve[{D[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],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{3} e^{-2 x^2} \left (2 e^{x^2} x+\sqrt {e^{2 x^2} \left (9-5 x^2\right )}\right ) \]