Internal problem ID [1511]
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 14.
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 }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y+3 \,{\mathrm e}^{2 x} \left (11+12 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 54
dsolve(diff(y(x),x$4)+3*diff(y(x),x$3)+diff(y(x),x$2)-3*diff(y(x),x)-2*y(x)=-3*exp(2*x)*(11+12*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (x -1\right ) \left (-36 \,{\mathrm e}^{2 x} x -33 \,{\mathrm e}^{2 x}\right )}{36 x +33}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{-x}+c_{4} x \,{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 43
DSolve[y''''[x]+3*y'''[x]+y''[x]-3*y'[x]-2*y[x]==-3*Exp[2*x]*(11+12*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (-e^{4 x} (x-1)+e^x (c_3 x+c_2)+c_4 e^{3 x}+c_1\right ) \\ \end{align*}