Internal problem ID [1493]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant
coefficient. Page 483
Problem number: section 9.2, problem 43(b).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 61
dsolve(diff(y(x),x$4)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (-{\mathrm e}^{-\frac {\sqrt {2}\, x}{2}} c_{1} -{\mathrm e}^{\frac {\sqrt {2}\, x}{2}} c_{2} \right ) \sin \left (\frac {\sqrt {2}\, x}{2}\right )+\left (c_{3} {\mathrm e}^{-\frac {\sqrt {2}\, x}{2}}+c_{4} {\mathrm e}^{\frac {\sqrt {2}\, x}{2}}\right ) \cos \left (\frac {\sqrt {2}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 65
DSolve[y''''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\frac {x}{\sqrt {2}}} \left (\left (c_1 e^{\sqrt {2} x}+c_2\right ) \cos \left (\frac {x}{\sqrt {2}}\right )+\left (c_4 e^{\sqrt {2} x}+c_3\right ) \sin \left (\frac {x}{\sqrt {2}}\right )\right ) \]