81.10.20 problem 14-20

Internal problem ID [21615]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 14. Second order homogeneous differential equations with constant coefficients. Page 297.
Problem number : 14-20
Date solved : Thursday, October 02, 2025 at 07:59:03 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-\frac {6 y^{\prime }}{5}+\frac {9 y}{25}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)-6/5*diff(y(x),x)+9/25*y(x) = 0; 
ic:=[y(0) = 1, D(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {3 x}{5}} \left (1+\frac {7 x}{5}\right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 21

ode=D[y[x],{x,2}]-6/5*D[y[x],x]+9/25*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{5} e^{3 x/5} (7 x+5) \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x)/25 - 6*Derivative(y(x), x)/5 + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\frac {7 x}{5} + 1\right ) e^{\frac {3 x}{5}} \]