38.4.29 problem 11 (a)

Internal problem ID [8328]
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 : Tuesday, September 30, 2025 at 05:26:39 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*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 43

ode:=diff(y(x),x) = y(x)-cos(1/2*Pi*x); 
ic:=[y(2) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 40

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

\begin{align*} y(x)&\to e^{x-2} \left (e^2 \int _2^x-e^{-K[1]} \cos \left (\frac {1}{2} \pi K[1]\right )dK[1]+2\right ) \end{align*}

✓ Sympy. Time used: 0.105 (sec). Leaf size: 53

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + cos(pi*x/2) + Derivative(y(x), x),0) 
ics = {y(2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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