76.27.1 problem Ex. 1

Internal problem ID [20161]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 73
Problem number : Ex. 1
Date solved : Thursday, October 02, 2025 at 05:33:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{4 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = exp(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{2 x} \left ({\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} c_1 +2 c_2 \right )}{2} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==Exp[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.119 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - exp(4*x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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