Internal problem ID [4377]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 22.
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 }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)+13*diff(y(x),x$2)-18*diff(y(x),x)+36*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (3 x \right )+c_{2} \cos \left (3 x \right )+c_{3} {\mathrm e}^{x} \sin \left (\sqrt {3}\, x \right )+c_{4} {\mathrm e}^{x} \cos \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 47
DSolve[y''''[x]-2*y'''[x]+13*y''[x]-18*y'[x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 \cos (3 x)+c_4 \sin (3 x)+e^x \left (c_2 \cos \left (\sqrt {3} x\right )+c_1 \sin \left (\sqrt {3} x\right )\right ) \\ \end{align*}