2.7.25 problem 41

Internal problem ID [831]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 41
Date solved : Tuesday, September 30, 2025 at 04:15:54 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime }-7 y^{\prime }-20 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=6*diff(diff(y(x),x),x)-7*diff(y(x),x)-20*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-\frac {4 x}{3}}+c_2 \,{\mathrm e}^{\frac {5 x}{2}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 26

ode=6*D[y[x],{x,2}]-7*D[y[x],x]-20*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-4 x/3}+c_2 e^{5 x/2} \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-20*y(x) - 7*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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