58.10.30 problem 30

Internal problem ID [14717]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 30
Date solved : Thursday, October 02, 2025 at 09:50:27 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ y^{\prime }\left (0\right )&=9 \\ \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 14

ode:=4*diff(diff(y(x),x),x)-12*diff(y(x),x)+9*y(x) = 0; 
ic:=[y(0) = 4, D(y)(0) = 9]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

ode=4*D[y[x],{x,2}]-12*D[y[x],x]+9*y[x]==0; 
ic={y[0]==4,Derivative[1][y][0] ==9}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{3 x/2} (3 x+4) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 12*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 4, Subs(Derivative(y(x), x), x, 0): 9} 
dsolve(ode,func=y(x),ics=ics)
 

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