Internal problem ID [13320]
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 (h).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime \prime \prime }+15 y^{\prime \prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(4*diff(y(x),x$4)+15*diff(y(x),x$2)-4*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{\frac {x}{2}}+c_{2} {\mathrm e}^{-\frac {x}{2}}+c_{3} \sin \left (2 x \right )+c_{4} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 37
DSolve[4*y''''[x]+15*y''[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} \left (c_4 e^x+c_3\right )+c_1 \cos (2 x)+c_2 \sin (2 x) \]