44.4.29 problem 11 (a)

Internal problem ID [7042]
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 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 11 (a)
Date solved : Monday, January 27, 2025 at 02:42:10 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 43

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

\[ y = \frac {2 \pi ^{2} {\mathrm e}^{x -2}-2 \pi \sin \left (\frac {\pi x}{2}\right )+4 \cos \left (\frac {\pi x}{2}\right )+12 \,{\mathrm e}^{x -2}}{\pi ^{2}+4} \]

✓ Solution by Mathematica

Time used: 0.103 (sec). Leaf size: 52

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

\[ y(x)\to \frac {2 \left (6+\pi ^2\right ) e^x-2 e^2 \pi \sin \left (\frac {\pi x}{2}\right )+4 e^2 \cos \left (\frac {\pi x}{2}\right )}{e^2 \left (4+\pi ^2\right )} \]