Internal problem ID [11690]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime }=-8} \] With initial conditions \begin {align*} [y \left (3\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 45
dsolve([2*(y(x)^2+4)+(1-x^2)*y(x)*diff(y(x),x)=0,y(3) = 0],y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {2 \sqrt {3 x^{2}-10 x +3}}{1+x} \\ y \left (x \right ) &= \frac {2 \sqrt {3 x^{2}-10 x +3}}{1+x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.886 (sec). Leaf size: 51
DSolve[{2*(y[x]^2+4)+(1-x^2)*y[x]*y'[x]==0,{y[3]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 \sqrt {3 x^2-10 x+3}}{x+1} \\ y(x)\to \frac {2 \sqrt {3 x^2-10 x+3}}{x+1} \\ \end{align*}