What is the solution for (y^3-1)e^x+3y^2(e^x+1)(dy)/(dx)=0,y(0)=2 ?

The solution for (y^3-1)e^x+3y^2(e^x+1)(dy)/(dx)=0,y(0)=2 is y=\sqrt[3]{(e^x+15)/(e^x+1)}

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(y^3-1)e^x+3y^2(e^x+1)(dy)/(dx)=0,y(0)=2

(y^{3} - 1) e^{x} + 3 y^{2} (e^{x} + 1) \frac{d y}{d x} = 0, y (0) = 2

y = 3 \frac{e ^{x} + 15}{e ^{x} + 1}

Solution steps

(y^{3} - 1) e^{x} + 3 y^{2} (e^{x} + 1) \frac{d y}{d x} = 0

Solve separable ODE:

y = 3 \frac{e ^{x} + 15}{e ^{x} + 1}

y = 3 \frac{e ^{x} + 15}{e ^{x} + 1}

What is the solution for (y^3-1)e^x+3y^2(e^x+1)(dy)/(dx)=0,y(0)=2 ?
The solution for (y^3-1)e^x+3y^2(e^x+1)(dy)/(dx)=0,y(0)=2 is y=\sqrt[3]{(e^x+15)/(e^x+1)}