Internal problem ID [2617]
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]]
\[ \boxed {y^{\prime \prime \prime }=6 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1, y^{\prime \prime }\left (0\right ) = -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)
\[ y \left (x \right ) = \frac {1}{4} x^{4}-2 x^{2}+1-x \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 22
DSolve[{y'''[x]==6*x,{y[0]==2,y'[0]==-1,y''[0]==-4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (x^4-8 x^2-4 x+8\right ) \]