Internal problem ID [1555]
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 58.
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 }+9 y^{\prime \prime }+7 y^{\prime }+2 y-{\mathrm e}^{-x} \left (30+24 x \right )+{\mathrm e}^{-2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 72
dsolve(diff(y(x),x$4)+5*diff(y(x),x$3)+9*diff(y(x),x$2)+7*diff(y(x),x)+2*y(x)=exp(-x)*(30+24*x)-exp(-2*x),y(x), singsol=all)
\[ y \relax (x ) = -\left (-x^{4}-x^{3}-6 x +3 x^{2}+6-x \,{\mathrm e}^{-x}-3 \,{\mathrm e}^{-x}\right ) {\mathrm e}^{-x}+{\mathrm e}^{-2 x} c_{1}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{-x} x +c_{4} x^{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.201 (sec). Leaf size: 40
DSolve[y''''[x]+5*y'''[x]+9*y''[x]+7*y'[x]+2*y[x]==Exp[-x]*(30+24*x)-Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (e^x \left (x \left (x \left (x^2+x-3+c_4\right )+6+c_3\right )-6+c_2\right )+x+3+c_1\right ) \\ \end{align*}