87.10.8 problem 9

Internal problem ID [23409]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 79
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:41:24 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 17

ode:=3*diff(diff(y(x),x),x)+diff(y(x),x)-2*y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {4 \,{\mathrm e}^{-x}}{5}+\frac {6 \,{\mathrm e}^{\frac {2 x}{3}}}{5} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 25

ode=3*D[y[x],{x,2}]+D[y[x],x]-2*y[x]==0; 
ic={y[0]==2,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{5} e^{-x} \left (3 e^{5 x/3}+2\right ) \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {6 e^{\frac {2 x}{3}}}{5} + \frac {4 e^{- x}}{5} \]