Internal problem ID [1516]
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 19.
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 }+5 y^{\prime \prime \prime }-5 y^{\prime }-2 y-18 \,{\mathrm e}^{x} \left (2 x +5\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve(2*diff(y(x),x$4)+5*diff(y(x),x$3)+0*diff(y(x),x$2)-5*diff(y(x),x)-2*y(x)=18*exp(x)*(5+2*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (2+x \right ) \left (36 x \,{\mathrm e}^{x}+90 \,{\mathrm e}^{x}\right )}{36 x +90}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-x}+c_{4} {\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 47
DSolve[2*y''''[x]+5*y'''[x]+0*y''[x]-5*y'[x]-2*y[x]==18*Exp[x]*(5+2*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (c_1 e^{3 x/2}+c_3 e^x+e^{3 x} \left (x (x+2)-\frac {40}{9}+c_4\right )+c_2\right ) \\ \end{align*}