Internal problem ID [5914]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 1.3 Introduction– Linear equations of First Order. Page 38
Problem number: 1 (d).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _quadrature]]
\[ \boxed {y^{\prime \prime \prime }=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$3)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{60} x^{5}+\frac {1}{2} c_{1} x^{2}+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 25
DSolve[y'''[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^5}{60}+c_3 x^2+c_2 x+c_1 \]