Internal problem ID [1544]
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 47.
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 }+26 y^{\prime \prime }-40 y^{\prime }+25 y-{\mathrm e}^{2 x} \left (3 \cos \relax (x )-\left (3 x +1\right ) \sin \relax (x )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.415 (sec). Leaf size: 91
dsolve(1*diff(y(x),x$4)-8*diff(y(x),x$3)+26*diff(y(x),x$2)-40*diff(y(x),x)+25*y(x)=exp(2*x)*(3*cos(1*x)-(1+3*x)*sin(1*x)),y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {9 \,{\mathrm e}^{2 x}}{16}+\frac {{\mathrm e}^{2 x} x}{4}\right ) \cos \relax (x )+\left (-\frac {{\mathrm e}^{2 x}}{4}+\frac {3 \,{\mathrm e}^{2 x} x}{8}+\frac {{\mathrm e}^{2 x} x^{3}}{8}+\frac {{\mathrm e}^{2 x} x^{2}}{8}\right ) \sin \relax (x )+c_{1} {\mathrm e}^{2 x} \cos \relax (x )+c_{2} {\mathrm e}^{2 x} \sin \relax (x )+c_{3} {\mathrm e}^{2 x} \cos \relax (x ) x +c_{4} {\mathrm e}^{2 x} \sin \relax (x ) x \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 56
DSolve[1*y''''[x]-8*y'''[x]+26*y''[x]-40*y'[x]+25*y[x]==Exp[2*x]*(3*Cos[1*x]-(1+3*x)*Sin[1*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{16} e^{2 x} ((2 (1+8 c_4) x+3+16 c_3) \cos (x)+(x (2 x (x+1)+9+16 c_2)-1+16 c_1) \sin (x)) \\ \end{align*}