Internal problem ID [4163]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-y^{\prime }-x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0, y^{\prime }\relax (1) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.007 (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)
\[ y \relax (x ) = \frac {1}{3} x^{3}-x^{2}+\frac {2}{3} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 18
DSolve[{x*y''[x]-y'[x]==x^2,{y[1]==0,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left ((x-3) x^2+2\right ) \\ \end{align*}