67.17.31 problem 31

Internal problem ID [16852]
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 : 31
Date solved : Thursday, October 02, 2025 at 01:39:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&=98 x^{2} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)-9*diff(y(x),x)+14*y(x) = 98*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} c_2 +{\mathrm e}^{7 x} c_1 +7 x^{2}+9 x +\frac {67}{14} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 33

ode=D[y[x],{x,2}]-9*D[y[x],x]+14*y[x]==98*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 7 x^2+9 x+c_1 e^{2 x}+c_2 e^{7 x}+\frac {67}{14} \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-98*x**2 + 14*y(x) - 9*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{2 x} + C_{2} e^{7 x} + 7 x^{2} + 9 x + \frac {67}{14} \]