Internal problem ID [11608]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises
page 37
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 y x \right ) y^{\prime }=-2 \,{\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 29
dsolve([(y(x)*exp(x)+2*exp(x)+y(x)^2)+(exp(x)+2*x*y(x))*diff(y(x),x)=0,y(0) = 6],y(x), singsol=all)
\[ y \left (x \right ) = \frac {-{\mathrm e}^{x}+\sqrt {{\mathrm e}^{2 x}-8 \,{\mathrm e}^{x} x +32 x}}{2 x} \]
✓ Solution by Mathematica
Time used: 32.264 (sec). Leaf size: 37
DSolve[{(y[x]*Exp[x]+2*Exp[x]+y[x]^2)+(Exp[x]+2*x*y[x])*y'[x]==0,{y[0]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {-8 e^x x+32 x+e^{2 x}}-e^x}{2 x} \]