86.8.8 problem 8

Internal problem ID [23168]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5e at page 91
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:23:43 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} z^{\prime \prime }+2 z^{\prime }&=3 \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=diff(diff(z(x),x),x)+2*diff(z(x),x) = 3*sin(x); 
dsolve(ode,z(x), singsol=all);
 

\[ z = -\frac {{\mathrm e}^{-2 x} c_1}{2}-\frac {3 \sin \left (x \right )}{5}-\frac {6 \cos \left (x \right )}{5}+c_2 \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 31

ode=D[z[x],{x,2}]+2*D[z[x],x]==3*Sin[x]; 
ic={}; 
DSolve[{ode,ic},z[x],x,IncludeSingularSolutions->True]
 

\begin{align*} z(x)&\to -\frac {3 \sin (x)}{5}-\frac {6 \cos (x)}{5}-\frac {1}{2} c_1 e^{-2 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
z = Function("z") 
ode = Eq(-3*sin(x) + 2*Derivative(z(x), x) + Derivative(z(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=z(x),ics=ics)
 

\[ z{\left (x \right )} = C_{1} + C_{2} e^{- 2 x} - \frac {3 \sin {\left (x \right )}}{5} - \frac {6 \cos {\left (x \right )}}{5} \]