Internal problem ID [473]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\cos \relax (t ) y+\sin \relax (t ) y^{\prime }-{\mathrm e}^{t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = a] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 20
dsolve([cos(t)*y(t)+sin(t)*diff(y(t),t) = exp(t),y(1) = a],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{t}+a \sin \relax (1)-{\mathrm e}}{\sin \relax (t )} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 19
DSolve[{Cos[t]*y[t]+Sin[t]*y'[t] == Exp[t],y[1]==a},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \csc (t) \left (a \sin (1)+e^t-e\right ) \\ \end{align*}