7.8.29 problem 42

Internal problem ID [243]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 42
Date solved : Saturday, March 29, 2025 at 04:49:04 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 35 y^{\prime \prime }-y^{\prime }-12 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=35*diff(diff(y(x),x),x)-diff(y(x),x)-12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {3 x}{5}}+c_2 \,{\mathrm e}^{-\frac {4 x}{7}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 26

ode=35*D[y[x],{x,2}]-D[y[x],x]-12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{-4 x/7}+c_2 e^{3 x/5} \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} e^{- \frac {4 x}{7}} + C_{2} e^{\frac {3 x}{5}} \]