Internal problem ID [4014]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.1, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {2 y y^{\prime } x +\left (x +1\right ) y^{2}-{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 59
dsolve(2*x*y(x)*diff(y(x),x)+(1+x)*y(x)^2=exp(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {{\mathrm e}^{-x} \sqrt {2}\, \sqrt {x \,{\mathrm e}^{x} \left ({\mathrm e}^{2 x}+2 c_{1}\right )}}{2 x} \\ y \relax (x ) = \frac {{\mathrm e}^{-x} \sqrt {2}\, \sqrt {x \,{\mathrm e}^{x} \left ({\mathrm e}^{2 x}+2 c_{1}\right )}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.792 (sec). Leaf size: 66
DSolve[2*x*y[x]*y'[x]+(1+x)*y[x]^2==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {e^x+2 c_1 e^{-x}}}{\sqrt {2} \sqrt {x}} \\ y(x)\to \frac {\sqrt {e^x+2 c_1 e^{-x}}}{\sqrt {2} \sqrt {x}} \\ \end{align*}