74.7.33 problem 33

Internal problem ID [16110]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 08:41:50 AM
CAS classification : [_Bernoulli]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.111 (sec). Leaf size: 16

dsolve([diff(y(t),t)+2*y(t)=t^2*sqrt(y(t)),y(0) = 1],y(t), singsol=all)
 

\[ y = \frac {\left (t^{2}-2 t +2\right )^{2}}{4} \]

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 48

DSolve[{D[y[t],t]+2*y[t]==t^2*Sqrt[y[t]],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {1}{4} \left (t^2-2 t+2\right )^2 \\ y(t)\to \frac {1}{4} e^{-2 t} \left (e^t \left (t^2-2 t+2\right )-4\right )^2 \\ \end{align*}