Internal problem ID [540]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+b \sqrt {y}-a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 22
dsolve(diff(y(t),t) = -b*y(t)^(1/2)+a*y(t),y(t), singsol=all)
\[ -\frac {b}{a}-{\mathrm e}^{\frac {a t}{2}} c_{1}+\sqrt {y \relax (t )} = 0 \]
✓ Solution by Mathematica
Time used: 0.704 (sec). Leaf size: 55
DSolve[y'[t] == -b*y[t]^(1/2)+a*y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^{-a c_1} \left (e^{\frac {a t}{2}}-b e^{\frac {a c_1}{2}}\right ){}^2}{a^2} \\ y(t)\to 0 \\ y(t)\to \frac {b^2}{a^2} \\ \end{align*}