Internal problem ID [988]
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: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-2 y-2 \sqrt {y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 16
dsolve([diff(y(x),x)-2*y(x)=2*y(x)^(1/2),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = 4 \,{\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}+1 \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 14
DSolve[{y'[x]-2*y[x]==2*y[x]^(1/2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (1-2 e^x\right )^2 \\ \end{align*}