Internal problem ID [13169]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.3 (b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime \prime }+2 y^{\prime \prime }=6 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x*diff(y(x),x$3)+2*diff(y(x),x$2)=6*x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{3}}{3}-c_{1} \ln \left (x \right )+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 25
DSolve[x*y'''[x]+2*y''[x]==6*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{3}+c_3 x-c_1 \log (x)+c_2 \]