74.4.59 problem 57 (c)

Internal problem ID [15952]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 57 (c)
Date solved : Tuesday, January 28, 2025 at 08:24:29 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.802 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 45

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

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