32.8.9 problem Exercise 21.11, page 231

Internal problem ID [5958]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined Coefficients
Problem number : Exercise 21.11, page 231
Date solved : Sunday, March 30, 2025 at 10:28:11 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }&=2 \,{\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x) = 2*exp(2*x)*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{3 x} c_1}{3}+\frac {{\mathrm e}^{2 x} \left (-\cos \left (x \right )-3 \sin \left (x \right )\right )}{5}+c_2 \]

✓ Mathematica. Time used: 0.229 (sec). Leaf size: 33

ode=D[y[x],{x,2}]-3*D[y[x],x]==2*Exp[2*x]*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{15} e^{2 x} \left (-9 \sin (x)-3 \cos (x)+5 c_1 e^x\right )+c_2 \]

✓ Sympy. Time used: 0.255 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*exp(2*x)*sin(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{3 x} - \frac {3 e^{2 x} \sin {\left (x \right )}}{5} - \frac {e^{2 x} \cos {\left (x \right )}}{5} \]