50.2.17 problem 3

Internal problem ID [7823]
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
Date solved : Monday, January 27, 2025 at 03:24:17 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \frac {y^{\prime \prime }}{y^{\prime }}&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 25

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

\[ y = -3 \Gamma \left (\frac {1}{3}, -\frac {x^{3}}{3}\right ) c_{2} \Gamma \left (\frac {2}{3}\right )+2 \pi \sqrt {3}\, c_{2} +c_{1} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 39

DSolve[D[y[x],{x,2}]/D[y[x],x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 \left (-x^3\right )^{2/3} \Gamma \left (\frac {1}{3},-\frac {x^3}{3}\right )}{3^{2/3} x^2}+c_2 \]