12.19.33 problem section 9.3, problem 33

Internal problem ID [2180]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 33
Date solved : Monday, January 27, 2025 at 05:43:06 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }+12 y&=8 \cos \left (2 x \right )-16 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.263 (sec). Leaf size: 39

dsolve(1*diff(y(x),x$3)+3*diff(y(x),x$2)+4*diff(y(x),x)+12*y(x)=8*cos(2*x)-16*sin(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (169 c_1 +104 x +56\right ) \cos \left (2 x \right )}{169}+\frac {\left (182 x +169 c_3 -136\right ) \sin \left (2 x \right )}{169}+{\mathrm e}^{-3 x} c_2 \]

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 47

DSolve[1*D[y[x],{x,3}]+3*D[y[x],{x,2}]+4*D[y[x],x]+12*y[x]==8*Cos[2*x]-16*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{169} \left (169 c_3 e^{-3 x}+(104 x+43+169 c_1) \cos (2 x)+(182 x-32+169 c_2) \sin (2 x)\right ) \]