44.4.30 problem 11 (b)

Internal problem ID [7043]
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 (b)
Date solved : Monday, January 27, 2025 at 02:42:12 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 (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 35

dsolve([diff(y(x),x)=y(x)-cos(Pi/2*x),y(-1) = 0],y(x), singsol=all)
 

\[ y = \frac {-2 \pi \,{\mathrm e}^{x +1}-2 \pi \sin \left (\frac {\pi x}{2}\right )+4 \cos \left (\frac {\pi x}{2}\right )}{\pi ^{2}+4} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 39

DSolve[{D[y[x],x]==y[x]-Cos[Pi/2*x],{y[-1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4 \cos \left (\frac {\pi x}{2}\right )-2 \pi \left (e^{x+1}+\sin \left (\frac {\pi x}{2}\right )\right )}{4+\pi ^2} \]