Internal problem ID [2108]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 39.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _quadrature]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-6 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1, y^{\prime \prime }\relax (0) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(x),x$3)=6*x,y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = -4],y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{4} x^{4}-2 x^{2}+1-x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[{y'''[x]==6*x,{y[0]==2,y'[0]==-1,y''[0]==-4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x \left (x^3-8 x-4\right )+2 \\ \end{align*}