83.11.3 problem 3

Internal problem ID [21992]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter VI. Linear equations with constant coefficients. Ex. XIII at page 106
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:21:30 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }-30 y^{\prime }+25 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=9*diff(diff(y(x),x),x)-30*diff(y(x),x)+25*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {5 x}{3}} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 20

ode=9*D[y[x],{x,2}]-30*D[y[x],x]+25*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.091 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) - 30*Derivative(y(x), x) + 9*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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