23.3.173 problem 175

Internal problem ID [5887]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 175
Date solved : Tuesday, September 30, 2025 at 02:05:48 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y-10 y^{\prime }+3 y^{\prime \prime }&=0 \end{align*}

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

ode:=3*y(x)-10*diff(y(x),x)+3*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 24

ode=3*y[x] - 10*D[y[x],x] + 3*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.086 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - 10*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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