Internal problem ID [1520]
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 23.
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 }-2 y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }+4 y-{\mathrm e}^{2 x} \left (18 x^{2}+33 x +13\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 77
dsolve(1*diff(y(x),x$4)-2*diff(y(x),x$3)-3*diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=exp(2*x)*(13+33*x+18*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} \left (x^{2}+x +1\right ) \left (18 \,{\mathrm e}^{2 x} x^{2}+33 \,{\mathrm e}^{2 x} x +13 \,{\mathrm e}^{2 x}\right )}{108 x^{2}+198 x +78}+{\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} x \,{\mathrm e}^{-x}+c_{4} {\mathrm e}^{2 x} x \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 50
DSolve[1*y''''[x]-2*y'''[x]-3*y''[x]+4*y'[x]+4*y[x]==Exp[2*x]*(13+33*x+18*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{54} e^{2 x} \left (9 x \left (x^3+x^2+x-2+6 c_4\right )+10+54 c_3\right )+e^{-x} (c_2 x+c_1) \\ \end{align*}