What is the solution for (dy)/(dt)=([2t])/([y+yt^2]) ?

The solution for (dy)/(dt)=([2t])/([y+yt^2]) is y=sqrt(2ln(1+t^2)+c_{1)},y=-sqrt(2ln(1+t^2)+c_{1)}

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(dy)/(dt)=([2t])/([y+yt^2])

\frac{d y}{d t} = \frac{[ 2 t ]}{[ y + y t ^{2} ]}

y = 2 ln (1 + t^{2}) + c_{1}, y = - 2 ln (1 + t^{2}) + c_{1}

Solution steps

\frac{d y}{d t} = \frac{[ 2 t ]}{[ y + y t ^{2} ]}

Solve separable ODE:

y = 2 ln (1 + t^{2}) + c_{1}, y = - 2 ln (1 + t^{2}) + c_{1}

y = 2 ln (1 + t^{2}) + c_{1}, y = - 2 ln (1 + t^{2}) + c_{1}

y^{^{'}} + 2 x y = 13 x

2 x (\frac{d y}{d x}) = y^{2}

\frac{d y}{d x} + \frac{x y}{1 - x ^{2}} = \frac{x y ^{2}}{1 - x ^{2}}

\frac{df}{d x} = - f (x)

y^{^{'}} = 2 x y (1 + y^{2})

What is the solution for (dy)/(dt)=([2t])/([y+yt^2]) ?
The solution for (dy)/(dt)=([2t])/([y+yt^2]) is y=sqrt(2ln(1+t^2)+c_{1)},y=-sqrt(2ln(1+t^2)+c_{1)}