74.7.34 problem 34

Internal problem ID [16111]
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 : 34
Date solved : Tuesday, January 28, 2025 at 08:41:51 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: 0.103 (sec). Leaf size: 42

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

\[ y = 1+4 \,{\mathrm e}^{2 t}+2 \left (-t^{2}-2 t -2\right ) {\mathrm e}^{t}+\frac {t^{4}}{4}+t^{3}+2 t^{2}+2 t \]

✓ Solution by Mathematica

Time used: 0.170 (sec). Leaf size: 71

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} e^{2 t} \left (\int _0^te^{-K[1]} K[1]^2dK[1]-2\right ){}^2 \\ y(t)\to \frac {1}{4} e^{2 t} \left (\int _0^te^{-K[1]} K[1]^2dK[1]+2\right ){}^2 \\ \end{align*}