35.6.15 problem 15

Internal problem ID [6165]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 15
Date solved : Monday, January 27, 2025 at 01:42:33 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 5 y^{\prime \prime }+12 y^{\prime }+20 y&=120 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 31

dsolve(5*diff(y(x),x$2)+12*diff(y(x),x)+20*y(x)=120*sin(2*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {6 x}{5}} \sin \left (\frac {8 x}{5}\right ) c_2 +{\mathrm e}^{-\frac {6 x}{5}} \cos \left (\frac {8 x}{5}\right ) c_1 -5 \cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 44

DSolve[5*D[y[x],{x,2}]+12*D[y[x],x]+20*y[x]==120*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -5 \cos (2 x)+c_2 e^{-6 x/5} \cos \left (\frac {8 x}{5}\right )+c_1 e^{-6 x/5} \sin \left (\frac {8 x}{5}\right ) \]