Internal problem ID [12513]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 143.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-4 y^{\prime \prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$5)-4*diff(y(x),x$3)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} x +c_{3} x^{2}+c_{4} {\mathrm e}^{2 x}+c_{5} {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 39
DSolve[y'''''[x]-4*y'''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} c_1 e^{2 x}-\frac {1}{8} c_2 e^{-2 x}+x (c_5 x+c_4)+c_3 \]