Internal problem ID [981]
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: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+2 y-2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(x^2*diff(y(x),x)+2*y(x)=2*exp(1/x)*y(x)^(1/2),y(x), singsol=all)
\[ \sqrt {y \relax (x )}-\left (-\frac {1}{x}+c_{1}\right ) {\mathrm e}^{\frac {1}{x}} = 0 \]
✓ Solution by Mathematica
Time used: 0.302 (sec). Leaf size: 39
DSolve[y'[x]+2*y[x]==2*Exp[1/x]*y[x]^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-2 x} \left (\int _1^x2 e^{K[1]+\frac {1}{K[1]}}dK[1]+2 c_1\right ){}^2 \\ \end{align*}