What is the solution for (dz)/(dt)=4te^{3z} ?

The solution for (dz)/(dt)=4te^{3z} is z=-(ln(-6t^2-c_{1}))/3

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(dz)/(dt)=4te^{3z}

\frac{d z}{d t} = 4 t e^{3 z}

z = - \frac{ln ( - 6 t ^{2} - c _{1} )}{3}

Solution steps

\frac{d z}{d t} = 4 t e^{3 z}

Solve separable ODE:

z = - \frac{ln ( - 6 t ^{2} - c _{1} )}{3}

z = - \frac{ln ( - 6 t ^{2} - c _{1} )}{3}

- 2 x e^{\frac{- H ( x ) x}{x}} d x + x^{2} d H (x) = 0

\frac{d y}{d t} y = arccot (4 t)

(3 x^{2} y - x^{2}) d x + d y = 0

y^{^{'}} = 5 x^{3} y^{\frac{1}{5}}, y (0) = 0

\frac{d y}{d x} = 7 x + 2 x y, y (0) = 1

What is the solution for (dz)/(dt)=4te^{3z} ?
The solution for (dz)/(dt)=4te^{3z} is z=-(ln(-6t^2-c_{1}))/3