Internal problem ID [1896]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {1+y^{2}-\frac {y^{\prime }}{x^{3} \left (x -1\right )}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 17
dsolve([(1+y(x)^2)=diff(y(x),x)/(x^3*(x-1)),y(2) = 0],y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\frac {1}{5} x^{5}-\frac {1}{4} x^{4}-\frac {12}{5}\right ) \]
✓ Solution by Mathematica
Time used: 0.336 (sec). Leaf size: 21
DSolve[{(1+y[x]^2)==y'[x]/(x^3*(x-1)),y[2]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (\frac {1}{20} \left (x^4 (4 x-5)-48\right )\right ) \\ \end{align*}