Internal problem ID [832]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.2, Higher order linear differential equations. Constant coefficients. page
180
Problem number: 18.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+6 y^{\prime \prime }+30 y^{\prime }-36 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 38
dsolve(diff(y(x),x$4)-7*diff(y(x),x$3)+6*diff(y(x),x$2)+30*diff(y(x),x)-36*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{3 x}+{\mathrm e}^{-2 x} c_{2}+c_{3} {\mathrm e}^{\left (3+\sqrt {3}\right ) x}+c_{4} {\mathrm e}^{-\left (-3+\sqrt {3}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 51
DSolve[y''''[x]-7*y'''[x]+6*y''[x]+30*y'[x]-36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\left (\left (\sqrt {3}-3\right ) x\right )}+c_2 e^{\left (3+\sqrt {3}\right ) x}+c_3 e^{-2 x}+c_4 e^{3 x} \\ \end{align*}