Internal problem ID [1553]
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 56.
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-2 \left (x +1\right ) {\mathrm e}^{x}-{\mathrm e}^{-2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 74
dsolve(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)=2*exp(x)*(1+x)+exp(-2*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-2 x} \left (18 x^{3} {\mathrm e}^{3 x}+18 x^{2} {\mathrm e}^{3 x}-36 x \,{\mathrm e}^{3 x}+27 x^{2}+20 \,{\mathrm e}^{3 x}+36 x +18\right )}{486}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{x} x +c_{4} {\mathrm e}^{-2 x} x \]
✓ Solution by Mathematica
Time used: 0.177 (sec). Leaf size: 58
DSolve[y''''[x]+2*y'''[x]-3*y''[x]-4*y'[x]+4*y[x]==2*Exp[x]*(1+x)+Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{243} e^x \left (9 x \left (x^2+x-2+27 c_4\right )+10+243 c_3\right )+\frac {1}{54} e^{-2 x} (x (3 x+4+54 c_2)+2+54 c_1) \\ \end{align*}