Internal problem ID [4655]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }-y^{\prime }=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.027 (sec). Leaf size: 24
DSolve[x*y''[x]-y'[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{3}+\frac {c_1 x^2}{2}+c_2 \]