10.4.9 problem 11

Internal problem ID [1190]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 11
Date solved : Monday, January 27, 2025 at 04:43:32 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=-b \sqrt {y}+a y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve(diff(y(t),t) = -b*y(t)^(1/2)+a*y(t),y(t), singsol=all)
 

\[ \frac {-{\mathrm e}^{\frac {a t}{2}} c_1 a +\sqrt {y}\, a -b}{a} = 0 \]

✓ Solution by Mathematica

Time used: 0.705 (sec). Leaf size: 55

DSolve[D[y[t],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*}