Internal problem ID [4671]
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]]
\[ \boxed {x y^{\prime \prime }-y^{\prime }=x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {1}{3} x^{3}-x^{2}+\frac {2}{3} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 19
DSolve[{x*y''[x]-y'[x]==x^2,{y[1]==0,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \left (x^3-3 x^2+2\right ) \]