15.14.7 problem 7

Internal problem ID [3179]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 7
Date solved : Tuesday, March 04, 2025 at 04:04:59 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

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

\[ y = {\mathrm e}^{\frac {\left (-3+\sqrt {17}\right ) x}{2}} c_2 +{\mathrm e}^{-\frac {\left (3+\sqrt {17}\right ) x}{2}} c_{1} -\frac {\sin \left (2 x \right )}{12}-\frac {\cos \left (2 x \right )}{12} \]

✓ Mathematica. Time used: 0.375 (sec). Leaf size: 52

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

\[ y(x)\to -\frac {1}{12} \cos (2 x)+e^{-\frac {1}{2} \left (3+\sqrt {17}\right ) x} \left (c_2 e^{\sqrt {17} x}+c_1\right )-\frac {1}{6} \sin (x) \cos (x) \]

✓ Sympy. Time used: 0.247 (sec). Leaf size: 42

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (-3 + \sqrt {17}\right )}{2}} + C_{2} e^{- \frac {x \left (3 + \sqrt {17}\right )}{2}} - \frac {\sin {\left (2 x \right )}}{12} - \frac {\cos {\left (2 x \right )}}{12} \]