Internal problem ID [4806]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page
414
Problem number: 28.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$4)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-x} \sin \left (x \right )+c_{2} {\mathrm e}^{-x} \cos \left (x \right )+c_{3} {\mathrm e}^{x} \sin \left (x \right )+c_{4} {\mathrm e}^{x} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 40
DSolve[y''''[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (\left (c_4 e^{2 x}+c_1\right ) \cos (x)+\left (c_3 e^{2 x}+c_2\right ) \sin (x)\right ) \]