83.17.4 problem 2 (b)

Internal problem ID [22050]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Examination II. page 256
Problem number : 2 (b)
Date solved : Thursday, October 02, 2025 at 08:23:12 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = -{\mathrm e}^{-x} c_1 -\frac {\sin \left (2 x \right )}{5}-\frac {\cos \left (2 x \right )}{10}+c_2 \]

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to -\frac {1}{5} \sin (2 x)-\frac {1}{10} \cos (2 x)+c_1 \left (-e^{-x}\right )+c_2 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} - \frac {\sin {\left (2 x \right )}}{5} - \frac {\cos {\left (2 x \right )}}{10} \]