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

The solution for (dx)/(dt)=2tsqrt(1-x^2) is x=sin(t^2+c_{1})

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(dx)/(dt)=2tsqrt(1-x^2)

\frac{d x}{d t} = 2 t 1 - x^{2}

x = sin (t^{2} + c_{1})

Solution steps

\frac{d x}{d t} = 2 t 1 - x^{2}

Solve separable ODE:

x = sin (t^{2} + c_{1})

x = sin (t^{2} + c_{1})

3 x [\frac{d y}{d x}] = 4 x y

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = 3 x^{2} - 5

4 y^{^{''}} + 36 y = csc (3 x)

y^{^{''}} - y = cosh (x)

y^{^{''}} - 4 y^{^{'}} = x e^{4 x}

What is the solution for (dx)/(dt)=2tsqrt(1-x^2) ?
The solution for (dx)/(dt)=2tsqrt(1-x^2) is x=sin(t^2+c_{1})