73.15.29 problem 22.10 (b)

Internal problem ID [15389]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.10 (b)
Date solved : Monday, March 31, 2025 at 01:36:18 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=4 x \,{\mathrm e}^{6 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)-10*y(x) = 4*x*exp(6*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{5 x} c_2 +{\mathrm e}^{-2 x} c_1 +\frac {\left (8 x -9\right ) {\mathrm e}^{6 x}}{16} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 36

ode=D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==4*x*Exp[6*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{16} e^{6 x} (8 x-9)+c_1 e^{-2 x}+c_2 e^{5 x} \]

✓ Sympy. Time used: 0.269 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*exp(6*x) - 10*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{5 x} + \frac {\left (8 x - 9\right ) e^{6 x}}{16} \]