74.7.5 problem 5

Internal problem ID [16003]
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 : 5
Date solved : Thursday, March 13, 2025 at 07:11:45 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }-2 y&=\frac {\cos \left (t \right )}{\sqrt {y}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(y(t),t)-2*y(t) = 1/y(t)^(1/2)*cos(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y^{{3}/{2}}+\frac {9 \cos \left (t \right )}{20}-\frac {3 \sin \left (t \right )}{20}-c_{1} {\mathrm e}^{3 t} = 0 \]

✓ Mathematica. Time used: 9.402 (sec). Leaf size: 45

ode=D[y[t],t]-2*y[t]==y[t]^(-1/2)*Cos[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {\left (e^{3 t} \left (3 \int _1^te^{-3 K[1]} \cos (K[1])dK[1]+2 c_1\right )\right ){}^{2/3}}{2^{2/3}} \]

✓ Sympy. Time used: 30.228 (sec). Leaf size: 99

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-2*y(t) + Derivative(y(t), t) - cos(t)/sqrt(y(t)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = \frac {\left (-1 + \sqrt {3} i\right ) \left (C_{1} e^{3 t} + \frac {3 \sin {\left (t \right )}}{20} - \frac {9 \cos {\left (t \right )}}{20}\right )^{\frac {2}{3}}}{2}, \ y{\left (t \right )} = \frac {\left (-1 - \sqrt {3} i\right ) \left (C_{1} e^{3 t} + \frac {3 \sin {\left (t \right )}}{20} - \frac {9 \cos {\left (t \right )}}{20}\right )^{\frac {2}{3}}}{2}, \ y{\left (t \right )} = \left (C_{1} e^{3 t} + \frac {3 \sin {\left (t \right )}}{20} - \frac {9 \cos {\left (t \right )}}{20}\right )^{\frac {2}{3}}\right ] \]