Internal problem ID [12516]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 146.
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)
\[ y \left (x \right ) = \left (-c_{1} {\mathrm e}^{-\frac {x \sqrt {2}}{2}}-c_{2} {\mathrm e}^{\frac {x \sqrt {2}}{2}}\right ) \sin \left (\frac {x \sqrt {2}}{2}\right )+\left (c_{3} {\mathrm e}^{-\frac {x \sqrt {2}}{2}}+c_{4} {\mathrm e}^{\frac {x \sqrt {2}}{2}}\right ) \cos \left (\frac {x \sqrt {2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 65
DSolve[y''''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-\frac {x}{\sqrt {2}}} \left (\left (c_1 e^{\sqrt {2} x}+c_2\right ) \cos \left (\frac {x}{\sqrt {2}}\right )+\left (c_4 e^{\sqrt {2} x}+c_3\right ) \sin \left (\frac {x}{\sqrt {2}}\right )\right ) \]