83.12.1 problem 1

Internal problem ID [19094]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (D) at page 37
Problem number : 1
Date solved : Thursday, March 13, 2025 at 01:40:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (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);
 

\[ y \left (x \right ) = {\mathrm e}^{2 x} c_{2} +{\mathrm e}^{3 x} c_{1} +\frac {{\mathrm e}^{4 x}}{2} \]

✓ Mathematica. Time used: 0.022 (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]
 

\[ y(x)\to \frac {1}{2} e^{2 x} \left (e^{2 x}+2 c_2 e^x+2 c_1\right ) \]

✓ Sympy. Time used: 0.201 (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)
 

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