23.3.17 problem 8(g)

Internal problem ID [4158]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 8(g)
Date solved : Sunday, March 30, 2025 at 02:41:14 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)-6*diff(y(x),x)+9*y(x) = exp(x)*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (\frac {4 \cos \left (x \right )}{25}+\frac {3 \sin \left (x \right )}{25}+\left (c_1 x +c_2 \right ) {\mathrm e}^{2 x}\right ) \]

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 35

ode=D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==Exp[x]*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{25} e^x \left (3 \sin (x)+4 \cos (x)+25 e^{2 x} (c_2 x+c_1)\right ) \]

✓ Sympy. Time used: 0.258 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - exp(x)*sin(x) - 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\left (C_{1} + C_{2} x\right ) e^{2 x} + \frac {3 \sin {\left (x \right )}}{25} + \frac {4 \cos {\left (x \right )}}{25}\right ) e^{x} \]