8.9.4 problem 4

Internal problem ID [848]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 4
Date solved : Tuesday, March 04, 2025 at 11:53:42 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3 y&=0 \end{align*}

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

ode:=2*diff(diff(y(x),x),x)-7*diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

ode=2*D[y[x],{x,2}]-7*D[y[x],x]+3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.149 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) - 7*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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