76.33.27 problem Ex. 27

Internal problem ID [20205]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 27
Date solved : Thursday, October 02, 2025 at 05:34:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 20 y-9 y^{\prime }+y^{\prime \prime }&=20 x \end{align*}

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

ode:=diff(diff(y(x),x),x)-9*diff(y(x),x)+20*y(x) = 20*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} c_2 +{\mathrm e}^{4 x} c_1 +x +\frac {9}{20} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 26

ode=D[y[x],{x,2}]-9*D[y[x],x]+20*y[x]==20*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x+c_1 e^{4 x}+c_2 e^{5 x}+\frac {9}{20} \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-20*x + 20*y(x) - 9*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{4 x} + C_{2} e^{5 x} + x + \frac {9}{20} \]