73.12.9 problem 19.2 (c)

Internal problem ID [15361]
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)
Date solved : Tuesday, January 28, 2025 at 07:53:47 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-8 y^{\prime \prime }+37 y^{\prime }-50 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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[D[y[x],{x,3}]-8*D[y[x],{x,2}]+37*D[y[x],x]-50*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (c_2 e^x \cos (4 x)+c_1 e^x \sin (4 x)+c_3\right ) \]