67.12.9 problem 19.2 (c)

Internal problem ID [16648]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.2 (c)
Date solved : Thursday, October 02, 2025 at 01:37:21 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-8 y^{\prime \prime }+37 y^{\prime }-50 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=diff(diff(diff(y(x),x),x),x)-8*diff(diff(y(x),x),x)+37*diff(y(x),x)-50*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 +c_2 \,{\mathrm e}^{x} \sin \left (4 x \right )+c_3 \,{\mathrm e}^{x} \cos \left (4 x \right )\right ) {\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 34

ode=D[y[x],{x,3}]-8*D[y[x],{x,2}]+37*D[y[x],x]-50*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 x} \left (c_2 e^x \cos (4 x)+c_1 e^x \sin (4 x)+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-50*y(x) + 37*Derivative(y(x), x) - 8*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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