76.2.26 problem 26

Internal problem ID [17362]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 10:02:27 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.077 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 19

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

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