12.19.37 problem section 9.3, problem 37

Internal problem ID [2184]
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 37
Date solved : Monday, January 27, 2025 at 05:43:11 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 47

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

\[ y = -\frac {{\mathrm e}^{-2 x} \left (\left (\cos \left (x \right )+7 \sin \left (x \right )\right ) {\mathrm e}^{3 x}-10 c_3 \cos \left (x \right ) {\mathrm e}^{x}-10 c_4 \sin \left (x \right ) {\mathrm e}^{x}-10 c_2 \,{\mathrm e}^{4 x}-10 c_1 \right )}{10} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 56

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

\[ y(x)\to c_3 e^{-2 x}+c_4 e^{2 x}-\frac {1}{10} e^x (7 \sin (x)+\cos (x))+c_2 e^{-x} \cos (x)+c_1 e^{-x} \sin (x) \]