What is the solution for y=t^2ln(t^2)(dy)/(dt) ?

The solution for y=t^2ln(t^2)(dy)/(dt) is y=e^{1/2 \Ei(-ln(t))+c_{1}}

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y=t^2ln(t^2)(dy)/(dt)

y = t^{2} ln (t^{2}) \frac{d y}{d t}

y = e^{\frac{1}{2} Ei (- l n (t)) + c_{1}}

Solution steps

y = t^{2} ln (t^{2}) \frac{d y}{d t}

Solve separable ODE:

y = e^{\frac{1}{2} Ei (- l n (t)) + c_{1}}

y = e^{\frac{1}{2} Ei (- l n (t)) + c_{1}}

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

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

\frac{d y}{d x} = \frac{3 x ^{2} - 4 x - 1}{2 y - 4}

\frac{d y}{d x} = \frac{e ^{y}}{x}

\frac{d y}{d x} = \frac{10 + 12 x}{x y ^{2}}, y (1) = 5

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