73.17.46 problem 46

Internal problem ID [15509]
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 : 46
Date solved : Monday, March 31, 2025 at 01:39:58 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 3 y^{\prime \prime }+8 y^{\prime }-3 y&=123 x \sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 39

ode:=3*diff(diff(y(x),x),x)+8*diff(y(x),x)-3*y(x) = 123*x*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-3 x} c_2 +{\mathrm e}^{\frac {x}{3}} c_1 +\frac {\left (-492 x -241\right ) \cos \left (3 x \right )}{246}+\frac {\left (-205 x +108\right ) \sin \left (3 x \right )}{82} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 50

ode=3*D[y[x],{x,2}]+8*D[y[x],x]-3*y[x]==123*x*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \left (\frac {54}{41}-\frac {5 x}{2}\right ) \sin (3 x)+\left (-2 x-\frac {241}{246}\right ) \cos (3 x)+c_1 e^{x/3}+c_2 e^{-3 x} \]

✓ Sympy. Time used: 0.306 (sec). Leaf size: 51

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-123*x*sin(3*x) - 3*y(x) + 8*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 3 x} + C_{2} e^{\frac {x}{3}} - \frac {5 x \sin {\left (3 x \right )}}{2} - 2 x \cos {\left (3 x \right )} + \frac {54 \sin {\left (3 x \right )}}{41} - \frac {241 \cos {\left (3 x \right )}}{246} \]