Internal problem ID [1543]
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 46.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y-{\mathrm e}^{2 x} \left (\cos \left (2 x \right )-\sin \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 103
dsolve(1*diff(y(x),x$4)-8*diff(y(x),x$3)+32*diff(y(x),x$2)-64*diff(y(x),x)+64*y(x)=exp(2*x)*(cos(2*x)-sin(2*x)),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {3 \,{\mathrm e}^{2 x} x}{64}-\frac {{\mathrm e}^{2 x} x^{2}}{32}+\frac {41 \,{\mathrm e}^{2 x}}{128}\right ) \cos \left (2 x \right )+\left (\frac {{\mathrm e}^{2 x} x}{64}+\frac {{\mathrm e}^{2 x} x^{2}}{32}+\frac {3 \,{\mathrm e}^{2 x}}{64}\right ) \sin \left (2 x \right )+c_{1} \cos \left (2 x \right ) {\mathrm e}^{2 x}+c_{2} \sin \left (2 x \right ) {\mathrm e}^{2 x}+c_{3} x \cos \left (2 x \right ) {\mathrm e}^{2 x}+c_{4} x \,{\mathrm e}^{2 x} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.119 (sec). Leaf size: 59
DSolve[1*y''''[x]-8*y'''[x]+32*y''[x]-64*y'[x]+64*y[x]==Exp[2*x]*(Cos[2*x]-Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{256} e^{2 x} ((4 x (-2 x+1+64 c_4)+5+256 c_3) \cos (2 x)+(8 x (x+1+32 c_2)-1+256 c_1) \sin (2 x)) \\ \end{align*}