Internal problem ID [6155]
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]]
\[ \boxed {0=-\frac {y^{\prime \prime }}{y^{\prime }}+x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)/diff(y(x),x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = -3 \Gamma \left (\frac {1}{3}, -\frac {x^{3}}{3}\right ) c_{2} \Gamma \left (\frac {2}{3}\right )+2 \sqrt {3}\, \pi c_{2} +c_{1} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 39
DSolve[y''[x]/y'[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1 \left (-x^3\right )^{2/3} \Gamma \left (\frac {1}{3},-\frac {x^3}{3}\right )}{3^{2/3} x^2}+c_2 \]