35.6.12 problem 12

Internal problem ID [6162]
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 : 12
Date solved : Monday, January 27, 2025 at 01:40:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+12 y&=80 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 43

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+12*y(x)=80*sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 52

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+12*y[x]==80*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

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