Internal problem ID [13305]
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: 19.2 (c).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-8 y^{\prime \prime }+37 y^{\prime }-50 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$3)-8*diff(y(x),x$2)+37*diff(y(x),x)-50*y(x)=0,y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{3 x} \sin \left (4 x \right )+c_{3} {\mathrm e}^{3 x} \cos \left (4 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 34
DSolve[y'''[x]-8*y''[x]+37*y'[x]-50*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (c_2 e^x \cos (4 x)+c_1 e^x \sin (4 x)+c_3\right ) \]