73.7.41 problem 41

Internal problem ID [15120]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 41
Date solved : Thursday, March 13, 2025 at 05:41:01 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(y(x),x)+2*y(x) = sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\cos \left (x \right )}{5}+\frac {2 \sin \left (x \right )}{5}+c_{1} {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 31

ode=D[y[x],x]+2*y[x]==Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (\int _1^xe^{2 K[1]} \sin (K[1])dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.139 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + \frac {2 \sin {\left (x \right )}}{5} - \frac {\cos {\left (x \right )}}{5} \]