Internal problem ID [13316]
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: 19.4 (d).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$4)+13*diff(y(x),x$2)+36*y(x)=0,y(x), singsol=all)
\[ y = c_{1} \sin \left (2 x \right )+c_{2} \cos \left (2 x \right )+c_{3} \sin \left (3 x \right )+c_{4} \cos \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 34
DSolve[y''''[x]+13*y''[x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 \cos (2 x)+c_1 \cos (3 x)+c_4 \sin (2 x)+c_2 \sin (3 x) \]