32.10.21 problem Exercise 35.21, page 504

Internal problem ID [6015]
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 35.21, page 504
Date solved : Monday, January 27, 2025 at 01:32:34 PM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 16

dsolve([x*diff(y(x),x$2)-diff(y(x),x)=x^2,y(1) = 0, D(y)(1) = -1],y(x), singsol=all)
 

\[ y = \frac {1}{3} x^{3}-x^{2}+\frac {2}{3} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 19

DSolve[{x*D[y[x],{x,2}]-D[y[x],x]==x^2,{y[1]==0,Derivative[1][y][1]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

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