What is the solution for (dz)/(dt)=6te^{5z},t(0)=0 ?

The solution for (dz)/(dt)=6te^{5z},t(0)=0 is z=-(ln(-15t^2-c_{1}))/5

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(dz)/(dt)=6te^{5z},t(0)=0

\frac{d z}{d t} = 6 t e^{5 z}, t (0) = 0

z = - \frac{ln ( - 15 t ^{2} - c _{1} )}{5}

Solution steps

\frac{d z}{d t} = 6 t e^{5 z}

Solve separable ODE:

z = - \frac{ln ( - 15 t ^{2} - c _{1} )}{5}

z = - \frac{ln ( - 15 t ^{2} - c _{1} )}{5}

\frac{d x}{d y} = \frac{4 x ln ( x )}{y}

\frac{d x}{d t} = \frac{3}{x e ^{t + 6 x}}

y^{^{'}} + 2 x y^{2} = 0, y (\frac{1}{2}) = - 4

y^{^{'}} csc (t) = \frac{- y ^{15}}{14}

\frac{d x}{d t} = \frac{1}{x e ^{t + 7 x}}

What is the solution for (dz)/(dt)=6te^{5z},t(0)=0 ?
The solution for (dz)/(dt)=6te^{5z},t(0)=0 is z=-(ln(-15t^2-c_{1}))/5