72.7.13 problem 13

Internal problem ID [14683]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 13
Date solved : Monday, March 31, 2025 at 12:52:50 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\sin \left (t \right ) y+4 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(t),t) = sin(t)*y(t)+4; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (4 \int {\mathrm e}^{\cos \left (t \right )}d t +c_1 \right ) {\mathrm e}^{-\cos \left (t \right )} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 45

ode=D[y[t],t]==Sin[t]*y[t]+4; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \exp \left (\int _1^t\sin (K[1])dK[1]\right ) \left (\int _1^t4 \exp \left (-\int _1^{K[2]}\sin (K[1])dK[1]\right )dK[2]+c_1\right ) \]

✓ Sympy. Time used: 50.070 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)*sin(t) + Derivative(y(t), t) - 4,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ - \int y{\left (t \right )} e^{\cos {\left (t \right )}} \sin {\left (t \right )}\, dt - 4 \int e^{\cos {\left (t \right )}}\, dt = C_{1} \]