Internal problem ID [13297]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients.
Additional exercises page 369
Problem number: 19.1 (a).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)=0,y(x), singsol=all)
\[ y = c_{1} +c_{2} x +c_{3} x^{2}+c_{4} {\mathrm e}^{4 x} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 28
DSolve[y''''[x]-4*y'''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{64} c_1 e^{4 x}+x (c_4 x+c_3)+c_2 \]