68.4.59 problem 57 (c)

Internal problem ID [17239]
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 : Thursday, October 02, 2025 at 01:59:34 PM
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*}

✓ Maple. Time used: 0.407 (sec). Leaf size: 12

ode:=diff(y(t),t) = y(t)^(1/2)*cos(t); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 45

ode=D[y[t],t]==Sqrt[y[t]]*Cos[t]; 
ic={y[0]==1}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-sqrt(y(t))*cos(t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants