What is the solution for (dy)/(dt)=(2y)/(t+1) ?

The solution for (dy)/(dt)=(2y)/(t+1) is y=e^{c_{1}}t^2+2e^{c_{1}}t+e^{c_{1}}

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(dy)/(dt)=(2y)/(t+1)

\frac{d y}{d t} = \frac{2 y}{t + 1}

y = e^{c_{1}} t^{2} + 2 e^{c_{1}} t + e^{c_{1}}

Solution steps

\frac{d y}{d t} = \frac{2 y}{t + 1}

Solve separable ODE:

y = e^{c_{1}} t^{2} + 2 e^{c_{1}} t + e^{c_{1}}

y = e^{c_{1}} t^{2} + 2 e^{c_{1}} t + e^{c_{1}}

2 y y^{^{'}} = 3 t^{2}, y (0) = 7

y^{^{'}} = \frac{1}{2} (y^{2}) + 1

2 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = - 1

\frac{d x}{d t} = - x^{2} + 4 x

\frac{d x}{d t} + cos (t) x - cos (t) = 0

What is the solution for (dy)/(dt)=(2y)/(t+1) ?
The solution for (dy)/(dt)=(2y)/(t+1) is y=e^{c_{1}}t^2+2e^{c_{1}}t+e^{c_{1}}