83.13.1 problem 2

Internal problem ID [19106]
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 (E) at page 39
Problem number : 2
Date solved : Monday, March 31, 2025 at 06:48:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=2 \,{\mathrm e}^{\frac {5 x}{2}} \end{align*}

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

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = 2*exp(5/2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 +c_1 x +\frac {8 \,{\mathrm e}^{\frac {3 x}{2}}}{9}\right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 28

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

\[ y(x)\to \frac {8}{9} e^{5 x/2}+e^x (c_2 x+c_1) \]

✓ Sympy. Time used: 0.181 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{x} + \frac {8 e^{\frac {5 x}{2}}}{9} \]