83.16.2 problem 2

Internal problem ID [19112]
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 (H) at page 47
Problem number : 2
Date solved : Thursday, March 13, 2025 at 01:41:53 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 36

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

\[ y \left (x \right ) = \frac {{\mathrm e}^{2 x} \left (-\cos \left (x \right )+2 \sin \left (x \right )\right )}{10}+{\mathrm e}^{x} \left (\cos \left (2 x \right ) c_{1} +\sin \left (2 x \right ) c_{2} \right ) \]

✓ Mathematica. Time used: 0.194 (sec). Leaf size: 42

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

\[ y(x)\to \frac {1}{10} e^x \left (-e^x \cos (x)+10 c_2 \cos (2 x)+2 \sin (x) \left (e^x+10 c_1 \cos (x)\right )\right ) \]

✓ Sympy. Time used: 0.294 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (2 x \right )} + C_{2} \cos {\left (2 x \right )} + \frac {\left (2 \sin {\left (x \right )} - \cos {\left (x \right )}\right ) e^{x}}{10}\right ) e^{x} \]