23.3.22 problem 9(c)

Internal problem ID [4163]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 9(c)
Date solved : Tuesday, March 04, 2025 at 05:54:40 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 25 y^{\prime \prime }-30 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 15

ode:=25*diff(diff(y(x),x),x)-30*diff(y(x),x)+9*y(x) = 0; 
ic:=y(1) = 0, D(y)(1) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y \left (x \right ) = 2 \,{\mathrm e}^{-\frac {3}{5}+\frac {3 x}{5}} \left (x -1\right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 19

ode=25*D[y[x],{x,2}]-30*D[y[x],x]+9*y[x]==0; 
ic={y[1]==0,Derivative[1][y][1] ==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 2 e^{\frac {3 (x-1)}{5}} (x-1) \]

✓ Sympy. Time used: 0.173 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 30*Derivative(y(x), x) + 25*Derivative(y(x), (x, 2)),0) 
ics = {y(1): 0, Subs(Derivative(y(x), x), x, 1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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