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 : Monday, January 27, 2025 at 04:34:12 AM
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*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 18

dsolve([cos(t)*y(t)+sin(t)*diff(y(t),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: 0.056 (sec). Leaf size: 19

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

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