Internal problem ID [1538]
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 41.
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 }+3 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }-4 y+{\mathrm e}^{-x} \left (\cos \relax (x )-\sin \relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 57
dsolve(1*diff(y(x),x$4)+3*diff(y(x),x$3)+2*diff(y(x),x$2)-2*diff(y(x),x)-4*y(x)=-exp(-1*x)*(cos(x)-sin(x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-x} \left (5 x +14\right ) \cos \relax (x )}{50}+\frac {{\mathrm e}^{-x} \left (5 x -1\right ) \sin \relax (x )}{25}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-2 x}+c_{3} \cos \relax (x ) {\mathrm e}^{-x}+c_{4} \sin \relax (x ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 57
DSolve[1*y''''[x]+3*y'''[x]+2*y''[x]-2*y'[x]-4*y[x]==-Exp[-1*x]*(Cos[x]-Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{50} e^{-2 x} \left (50 \left (c_4 e^{3 x}+c_3\right )+e^x ((5 x+14+50 c_2) \cos (x)+(10 x-7+50 c_1) \sin (x))\right ) \\ \end{align*}