83.44.1 problem Ex 1 page 30

Internal problem ID [19458]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter III. Ordinary linear differential equations with constant coefficients
Problem number : Ex 1 page 30
Date solved : Monday, March 31, 2025 at 07:19:21 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+9 y^{\prime }-18 y&=0 \end{align*}

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

ode:=2*diff(diff(y(x),x),x)+9*diff(y(x),x)-18*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-6 x}+c_2 \,{\mathrm e}^{\frac {3 x}{2}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 24

ode=2*D[y[x],{x,2}]+9*D[y[x],x]-18*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{3 x/2}+c_2 e^{-6 x} \]

✓ Sympy. Time used: 0.146 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-18*y(x) + 9*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 6 x} + C_{2} e^{\frac {3 x}{2}} \]