Internal problem ID [1535]
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 38.
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 (2 \cos \left (2 x \right )-\sin \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
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(x)*(2*cos(2*x)-sin(2*x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{x} \cos \left (2 x \right )}{12}-\frac {{\mathrm e}^{x} \sin \left (2 x \right )}{12}+{\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} \cos \relax (x ) {\mathrm e}^{x}+c_{4} \sin \relax (x ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 51
DSolve[1*y''''[x]-3*y'''[x]+2*y''[x]+2*y'[x]-4*y[x]==Exp[x]*(2*Cos[2*x]-Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^{-x}+c_4 e^{2 x}+\frac {1}{12} e^x (\cos (2 x)+12 c_1 \sin (x)-2 \cos (x) (\sin (x)-6 c_2)) \\ \end{align*}