73.14.14 problem 21.13 (d)

Internal problem ID [15353]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.13 (d)
Date solved : Monday, March 31, 2025 at 01:35:11 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 31

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)-10*y(x) = 35*exp(5*x)+12*exp(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (35 x +7 c_2 -5\right ) {\mathrm e}^{5 x}}{7}+{\mathrm e}^{-2 x} c_1 -2 \,{\mathrm e}^{4 x} \]

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 36

ode=D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==35*Exp[5*x]+12*Exp[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -2 e^{4 x}+c_1 e^{-2 x}+e^{5 x} \left (5 x-\frac {5}{7}+c_2\right ) \]

✓ Sympy. Time used: 0.276 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*y(x) - 35*exp(5*x) - 12*exp(4*x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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