44.6.35 problem 35

Internal problem ID [7179]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 35
Date solved : Tuesday, February 04, 2025 at 12:44:40 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }-\sin \left (x \right ) y&=2 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 13

dsolve([diff(y(x),x)-sin(x)*y(x)=2*sin(x),y(1/2*Pi) = 1],y(x), singsol=all)
 

\[ y = -2+3 \,{\mathrm e}^{-\cos \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 15

DSolve[{D[y[x],x]-Sin[x]*y[x]==2*Sin[x],{y[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 e^{-\cos (x)}-2 \]