Internal problem ID [1552]
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 55.
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 }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y+{\mathrm e}^{x} \left (\sin \relax (x )+2 \cos \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.025 (sec). Leaf size: 63
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+11*diff(y(x),x$2)-14*diff(y(x),x)+10*y(x)=-exp(x)*(sin(x)+2*cos(2*x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \relax (x ) {\mathrm e}^{x}}{9}+\frac {7 \cos \left (2 x \right ) {\mathrm e}^{x}}{18}+\frac {\sin \left (2 x \right ) {\mathrm e}^{x} x}{6}+\frac {{\mathrm e}^{x} \cos \relax (x ) x}{6}+\cos \relax (x ) {\mathrm e}^{x} c_{1}+\sin \relax (x ) {\mathrm e}^{x} c_{2}+c_{3} {\mathrm e}^{x} \cos \left (2 x \right )+c_{4} \sin \left (2 x \right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 53
DSolve[y''''[x]-4*y'''[x]+11*y''[x]-14*y'[x]+10*y[x]==-Exp[x]*(Sin[x]+2*Cos[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{36} e^x ((11+36 c_2) \cos (2 x)+(1+36 c_3) \sin (x)+6 \cos (x) (x+2 (x+6 c_1) \sin (x)+6 c_4)) \\ \end{align*}