73.17.46 problem 46

Internal problem ID [15580]
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 : Tuesday, January 28, 2025 at 08:02:43 AM
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*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 45

dsolve(3*diff(y(x),x$2)+8*diff(y(x),x)-3*y(x)=123*x*sin(3*x),y(x), singsol=all)
 

\[ y = -2 \,{\mathrm e}^{-3 x} \left (-\frac {c_{1} {\mathrm e}^{\frac {10 x}{3}}}{2}+\left (\left (x +\frac {241}{492}\right ) \cos \left (3 x \right )+\sin \left (3 x \right ) \left (\frac {5 x}{4}-\frac {27}{41}\right )\right ) {\mathrm e}^{3 x}-\frac {c_{2}}{2}\right ) \]

✓ Solution by Mathematica

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

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

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