Internal problem ID [1539]
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 42.
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 }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y-{\mathrm e}^{x} \left (\cos \left (2 x \right )+\sin \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 61
dsolve(1*diff(y(x),x$4)-5*diff(y(x),x$3)+13*diff(y(x),x$2)-19*diff(y(x),x)+10*y(x)=exp(x)*(cos(2*x)+sin(2*x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (15 x +1\right ) {\mathrm e}^{x} \cos \left (2 x \right )}{200}-\frac {\left (10 x +39\right ) {\mathrm e}^{x} \sin \left (2 x \right )}{400}+\frac {{\mathrm e}^{x}}{8}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{x} \cos \left (2 x \right )+c_{4} {\mathrm e}^{x} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 53
DSolve[1*y''''[x]-5*y'''[x]+13*y''[x]-19*y'[x]+10*y[x]==Exp[x]*(Cos[2*x]+Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{400} e^x \left (400 \left (c_4 e^x+c_3\right )+(30 x-13+400 c_2) \cos (2 x)-2 (5 x+17-200 c_1) \sin (2 x)\right ) \\ \end{align*}