10.1.26 problem 26

Internal problem ID [1123]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 26
Date solved : Saturday, March 29, 2025 at 10:39:50 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 18

ode:=cos(t)*y(t)+sin(t)*diff(y(t),t) = exp(t); 
ic:=y(1) = a; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \left ({\mathrm e}^{t}+a \sin \left (1\right )-{\mathrm e}\right ) \csc \left (t \right ) \]

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 19

ode=Cos[t]*y[t]+Sin[t]*D[y[t],t] == Exp[t]; 
ic=y[1]==a; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \csc (t) \left (a \sin (1)+e^t-e\right ) \]

✓ Sympy. Time used: 0.322 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = \frac {a \sin {\left (1 \right )} + e^{t} - e}{\sin {\left (t \right )}} \]