Internal problem ID [1518]
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 21.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y-3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 68
dsolve(2*diff(y(x),x$4)+1*diff(y(x),x$3)-0*diff(y(x),x$2)-2*diff(y(x),x)-1*y(x)=3*exp(-x/2)*(1-6*x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {4 x \left (x +1\right ) \left (-18 \,{\mathrm e}^{-\frac {x}{2}} x +3 \,{\mathrm e}^{-\frac {x}{2}}\right )}{3 \left (6 x -1\right )}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{-\frac {x}{2}}+c_{3} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{4} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.28 (sec). Leaf size: 58
DSolve[2*y''''[x]+1*y'''[x]-0*y''[x]-2*y'[x]-1*y[x]==3*Exp[-x/2]*(1-6*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_4 e^x+e^{-x/2} \left (4 x (x+1)+c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} x}{2}\right )-8+c_3\right ) \\ \end{align*}