Internal problem ID [302]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with
Constant Coefficients. Page 300
Problem number: problem 30.
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 }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$4)-diff(y(x),x$3)+diff(y(x),x$2)-3*diff(y(x),x)-6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{2 x} c_{1}+{\mathrm e}^{-x} c_{2}+c_{3} \sin \left (\sqrt {3}\, x \right )+c_{4} \cos \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 44
DSolve[y''''[x]-y'''[x]+y''[x]-3*y'[x]-6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^{-x}+c_4 e^{2 x}+c_1 \cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \\ \end{align*}