73.15.28 problem 22.10 (a)

Internal problem ID [15388]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.10 (a)
Date solved : Monday, March 31, 2025 at 01:36:17 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&=\left (72 x^{2}-1\right ) {\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 32

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)-10*y(x) = (72*x^2-1)*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} c_2 +{\mathrm e}^{5 x} c_1 +{\mathrm e}^{2 x} \left (-6 x^{2}-x -1\right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 37

ode=D[y[x],{x,2}]-3*D[y[x],x]-10*y[x]==(72*x^2-1)*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -e^{2 x} \left (6 x^2+x+1\right )+c_1 e^{-2 x}+c_2 e^{5 x} \]

✓ Sympy. Time used: 0.296 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(72*x**2 - 1)*exp(2*x) - 10*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{5 x} + \left (- 6 x^{2} - x - 1\right ) e^{2 x} \]