Internal problem ID [14844]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 23.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(9*diff(y(x),x$3)+12*diff(y(x),x$2)+13*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{-\frac {2 x}{3}} \sin \left (x \right )+c_{3} {\mathrm e}^{-\frac {2 x}{3}} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 44
DSolve[9*y'''[x]+12*y''[x]+13*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3-\frac {3}{13} e^{-2 x/3} ((3 c_1+2 c_2) \cos (x)+(2 c_1-3 c_2) \sin (x)) \]