32.5.12 problem Exercise 11.11, page 97

Internal problem ID [5850]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.11, page 97
Date solved : Tuesday, March 04, 2025 at 11:48:21 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 26

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

\[ y(x)\to \frac {2 \sin (x)}{5}-\frac {\cos (x)}{5}+c_1 e^{-2 x} \]

✓ Sympy. Time used: 0.129 (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)
 

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