Internal problem ID [3408]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 669.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 40
dsolve((x^2+1)*(1+y(x)^2)*diff(y(x),x)+2*x*y(x)*(1-y(x))^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (\ln \left (x^{2}+1\right ) {\mathrm e}^{\textit {\_Z}}+2 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-\ln \left (x^{2}+1\right )-2 c_{1}-\textit {\_Z} -2\right )} \]
✓ Solution by Mathematica
Time used: 0.34 (sec). Leaf size: 40
DSolve[(1+x^2)(1+y[x]^2)y'[x]+2 x y[x](1-y[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\log (\text {$\#$1})-\frac {2}{\text {$\#$1}-1}\&\right ]\left [-\log \left (x^2+1\right )+c_1\right ] \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}