What is the solution for (dy)/(dt)+t/(y(t^2-1))=0 ?

The solution for (dy)/(dt)+t/(y(t^2-1))=0 is y=sqrt(-ln(t^2-1)+c_{1)},y=-sqrt(-ln(t^2-1)+c_{1)}

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(dy)/(dt)+t/(y(t^2-1))=0

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

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

Solution steps

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

Solve separable ODE:

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

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

x \frac{d x}{d y} = 4 y

\frac{d y}{y} = \frac{d x}{( 1 + x )}

d y - (y - 1)^{2} \cdot d x = 0

- 10 + 4 x + 5 \frac{d x}{d t} = 0

5 x y \frac{d y}{d x} = 2 x, y > 0

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