What is the solution for (dz)/(dt)+e^{2t+2z}=0 ?

The solution for (dz)/(dt)+e^{2t+2z}=0 is z=-(ln(e^{2t}-c_{1}))/2

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(dz)/(dt)+e^{2t+2z}=0

\frac{d z}{d t} + e^{2 t + 2 z} = 0

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

Solution steps

\frac{d z}{d t} + e^{2 t + 2 z} = 0

Solve separable ODE:

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

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

\frac{d y}{d x} = 4 x^{6} y

\frac{d y}{d x} = \frac{5 x ^{2}}{8 y ^{2}}

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

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

\frac{d x}{d y} = \frac{1 + x ^{2}}{y}

What is the solution for (dz)/(dt)+e^{2t+2z}=0 ?
The solution for (dz)/(dt)+e^{2t+2z}=0 is z=-(ln(e^{2t}-c_{1}))/2