What is the solution for 2x(dx)/(dt)-(x^2+1)=0 ?

The solution for 2x(dx)/(dt)-(x^2+1)=0 is x=sqrt(e^{t+c_{1)}-1},x=-sqrt(e^{t+c_{1)}-1}

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2x(dx)/(dt)-(x^2+1)=0

2 x \frac{d x}{d t} - (x^{2} + 1) = 0

x = e^{t + c_{1}} - 1, x = - e^{t + c_{1}} - 1

Solution steps

2 x \frac{d x}{d t} - (x^{2} + 1) = 0

Solve separable ODE:

x = e^{t + c_{1}} - 1, x = - e^{t + c_{1}} - 1

x = e^{t + c_{1}} - 1, x = - e^{t + c_{1}} - 1

\frac{d y}{d x} = \frac{2 y + 3}{x ^{2}}

(x y - 2 x + 4 y - 8) d y - (x y + 3 x - y - 3) d x = 0

y y^{^{'}} + 6 x = 0, y^{2} (0) = - 6 x^{2} + c, y (0) = 4

y^{^{'}} = - \frac{3}{7} e^{3 y}

x y^{^{'}} - 3 y + 2 = 0

What is the solution for 2x(dx)/(dt)-(x^2+1)=0 ?
The solution for 2x(dx)/(dt)-(x^2+1)=0 is x=sqrt(e^{t+c_{1)}-1},x=-sqrt(e^{t+c_{1)}-1}