74.7.6 problem 6

Internal problem ID [16004]
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 : 6
Date solved : Thursday, March 13, 2025 at 07:12:16 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+3 y&=\sqrt {y}\, \sin \left (t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(y(t),t)+3*y(t) = y(t)^(1/2)*sin(t); 
dsolve(ode,y(t), singsol=all);
 

\[ \sqrt {y}+\frac {2 \cos \left (t \right )}{13}-\frac {3 \sin \left (t \right )}{13}-{\mathrm e}^{-\frac {3 t}{2}} c_{1} = 0 \]

✓ Mathematica. Time used: 0.169 (sec). Leaf size: 40

ode=D[y[t],t]+3*y[t]==Sqrt[y[t]]*Sin[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{4} e^{-3 t} \left (\int _1^te^{\frac {3 K[1]}{2}} \sin (K[1])dK[1]+2 c_1\right ){}^2 \]

✓ Sympy. Time used: 0.695 (sec). Leaf size: 68

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-sqrt(y(t))*sin(t) + 3*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1}^{2} e^{- 3 t} + \frac {6 C_{1} e^{- \frac {3 t}{2}} \sin {\left (t \right )}}{13} - \frac {4 C_{1} e^{- \frac {3 t}{2}} \cos {\left (t \right )}}{13} + \frac {9 \sin ^{2}{\left (t \right )}}{169} - \frac {12 \sin {\left (t \right )} \cos {\left (t \right )}}{169} + \frac {4 \cos ^{2}{\left (t \right )}}{169} \]