78.13.1 problem 1 (a)

Internal problem ID [18252]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 18. The Method of Undetermined Coefficients. Problems at page 132
Problem number : 1 (a)
Date solved : Monday, March 31, 2025 at 05:23:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

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

\[ y = \frac {\left ({\mathrm e}^{9 x}+3 \,{\mathrm e}^{7 x} c_1 +3 c_2 \right ) {\mathrm e}^{-5 x}}{3} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 31

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

\[ y(x)\to \frac {e^{4 x}}{3}+c_1 e^{-5 x}+c_2 e^{2 x} \]

✓ Sympy. Time used: 0.185 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} e^{- 5 x} + C_{2} e^{2 x} + \frac {e^{4 x}}{3} \]