What is the solution for 1+t=2tx(dx)/(dt) ?

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

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1+t=2tx(dx)/(dt)

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

x = t + ln (t) + c_{1}, x = - t + ln (t) + c_{1}

Solution steps

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

Solve separable ODE:

x = t + ln (t) + c_{1}, x = - t + ln (t) + c_{1}

x = t + ln (t) + c_{1}, x = - t + ln (t) + c_{1}

2 y (x^{2} + 1) d y = x d x

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

\frac{x ^{2}}{y ^{2} - 1} y^{^{'}} = \frac{3 x ^{3}}{y}

y^{^{'}} = 9 y

(x + 1) \frac{d y}{d x} + y = 10

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