74.18.12 problem 18

Internal problem ID [16490]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 18
Date solved : Thursday, March 13, 2025 at 08:14:56 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 15 y^{\prime \prime }-11 y^{\prime }+2 y&=0 \end{align*}

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

ode:=15*diff(diff(y(x),x),x)-11*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} {\mathrm e}^{\frac {x}{3}}+c_{2} {\mathrm e}^{\frac {2 x}{5}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 26

ode=15*D[y[x],{x,2}]-11*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.172 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 11*Derivative(y(x), x) + 15*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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