Internal problem ID [2190]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 51.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 x y}{x^{2}+1}-x y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 23
dsolve([diff(y(x),x)+2*x/(1+x^2)*y(x)=x*y(x)^2,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {2}{\left (x^{2}+1\right ) \left (\ln \left (x^{2}+1\right )-2\right )} \]
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 24
DSolve[{y'[x]+2*x/(1+x^2)*y[x]==x*y[x]^2,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{\left (x^2+1\right ) \left (\log \left (x^2+1\right )-2\right )} \\ \end{align*}