73.17.45 problem 45

Internal problem ID [15508]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 45
Date solved : Monday, March 31, 2025 at 01:39:56 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=x \,{\mathrm e}^{\frac {3 x}{2}} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=4*diff(diff(y(x),x),x)-12*diff(y(x),x)+9*y(x) = x*exp(3/2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {3 x}{2}} \left (c_2 +c_1 x +\frac {1}{24} x^{3}\right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 29

ode=4*D[y[x],{x,2}]-12*D[y[x],x]+9*y[x]==x*Exp[3*x/2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{24} e^{3 x/2} \left (x^3+24 c_2 x+24 c_1\right ) \]

✓ Sympy. Time used: 0.262 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(3*x/2) + 9*y(x) - 12*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + \frac {x^{2}}{24}\right )\right ) e^{\frac {3 x}{2}} \]