2.9.3 problem 3

Internal problem ID [847]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 04:16:08 AM
CAS classification : [[_2nd_order, _missing_x]]

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

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

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

\[ y = \left (c_2 \,{\mathrm e}^{7 x}+c_1 \right ) {\mathrm e}^{-5 x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to e^{-5 x} \left (c_2 e^{7 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.089 (sec). Leaf size: 15

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

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