35.6.11 problem 11

Internal problem ID [6161]
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 : 11
Date solved : Monday, January 27, 2025 at 01:38:47 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=100 \cos \left (4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+10*y(x)=100*cos(4*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} \sin \left (3 x \right ) c_2 +{\mathrm e}^{-x} \cos \left (3 x \right ) c_1 +8 \sin \left (4 x \right )-6 \cos \left (4 x \right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 42

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+10*y[x]==100*Cos[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 8 \sin (4 x)-6 \cos (4 x)+c_2 e^{-x} \cos (3 x)+c_1 e^{-x} \sin (3 x) \]