12.5.14 problem 10

Internal problem ID [1638]
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
Date solved : Monday, January 27, 2025 at 05:15:30 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-2 y&=2 \sqrt {y} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 16

dsolve([diff(y(x),x)-2*y(x)=2*y(x)^(1/2),y(0) = 1],y(x), singsol=all)
 

\[ y = 4 \,{\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}+1 \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 14

DSolve[{D[y[x],x]-2*y[x]==2*y[x]^(1/2),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (1-2 e^x\right )^2 \]