67.15.11 problem 22.5 (a)

Internal problem ID [16729]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.5 (a)
Date solved : Thursday, October 02, 2025 at 01:38:15 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=-200 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)-10*y(x) = -200; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} c_2 +{\mathrm e}^{-2 x} c_1 +20 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 23

ode=D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==-200; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-2 x}+c_2 e^{5 x}+20 \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 200,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{5 x} + 20 \]