Internal problem ID [991]
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: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-y-\sqrt {y}\, x=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 26
dsolve([diff(y(x),x)-y(x)=x*y(x)^(1/2),y(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = \left (-8 x -16\right ) {\mathrm e}^{\frac {x}{2}}+x^{2}+4 x +16 \,{\mathrm e}^{x}+4 \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 28
DSolve[{y'[x]-y[x]==x*y[x]^(1/2),y[0]==4},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (x-4 e^{x/2}+2\right )^2 y(x)\to (x+2)^2 \end{align*}