Internal problem ID [4590]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 20. Constant
coefficients
Problem number: Exercise 20.20, page 220.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)-11*diff(y(x),x$2)-12*diff(y(x),x)+36*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\left (c_{2} x +c_{1} \right ) {\mathrm e}^{5 x}+x c_{4} +c_{3} \right ) {\mathrm e}^{-3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 35
DSolve[y''''[x]+2*y'''[x]-11*y''[x]-12*y'[x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (c_3 e^{5 x}+x \left (c_4 e^{5 x}+c_2\right )+c_1\right ) \]