Internal problem ID [1525]
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 28.
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 }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y-{\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 79
dsolve(1*diff(y(x),x$4)-7*diff(y(x),x$3)+18*diff(y(x),x$2)-20*diff(y(x),x)+8*y(x)=exp(2*x)*(3-8*x-5*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3} \left (x^{2}-x -2\right ) \left (-5 \,{\mathrm e}^{2 x} x^{2}-8 \,{\mathrm e}^{2 x} x +3 \,{\mathrm e}^{2 x}\right )}{60 x^{2}+96 x -36}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{2 x} x +c_{4} {\mathrm e}^{2 x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 55
DSolve[1*y''''[x]-7*y'''[x]+18*y''[x]-20*y'[x]+8*y[x]==Exp[2*x]*(3-8*x-5*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} e^{2 x} \left (x \left (x \left (x \left (-x^2+x+2\right )-6+12 c_4\right )+12 (1+c_3)\right )+12 (-1+c_2)\right )+c_1 e^x \\ \end{align*}