32.10.5 problem Exercise 35.5, page 504

Internal problem ID [5999]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.5, page 504
Date solved : Monday, January 27, 2025 at 01:30:42 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

\[ y \left (x \right ) = \frac {1}{3} x^{3}+\frac {1}{2} c_{1} x^{2}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 24

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

\[ y(x)\to \frac {x^3}{3}+\frac {c_1 x^2}{2}+c_2 \]