1.3 problem 1 (d)

Internal problem ID [5161]

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]]

Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-x^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(diff(y(x),x$3)=x^2,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {1}{60} x^{5}+\frac {1}{2} c_{1} x^{2}+c_{2} x +c_{3} \]

Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 25

DSolve[y'''[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^5}{60}+c_3 x^2+c_2 x+c_1 \\ \end{align*}