Internal problem ID [13512]
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: 13.6 (f).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime \prime }+2 y^{\prime \prime }=6 x} \] With initial conditions \begin {align*} [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = 1, y^{\prime \prime }\left (1\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([x*diff(y(x),x$3)+2*diff(y(x),x$2)=6*x,y(1) = 2, D(y)(1) = 1, (D@@2)(y)(1) = 4],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{3}}{3}-2 \ln \left (x \right )+2 x -\frac {1}{3} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 21
DSolve[{x*y'''[x]+2*y''[x]==6*x,{y[1]==2,y'[1]==1,y''[1]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left (x^3+6 x-6 \log (x)-1\right ) \]