Internal problem ID [5402]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page
12
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\frac {y^{\prime \prime }}{y^{\prime }}-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)/diff(y(x),x)=x^2,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+\left (2 \pi \sqrt {3}-3 \Gamma \left (\frac {1}{3}, -\frac {x^{3}}{3}\right ) \Gamma \left (\frac {2}{3}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 26
DSolve[y''[x]/y'[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\frac {1}{3} c_1 x E_{\frac {2}{3}}\left (-\frac {x^3}{3}\right ) \\ \end{align*}