Exercise
$\frac{dz}{dt}=-4e^{t-z}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dz/dt=-4e^(t-z). Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Group the terms of the differential equation. Move the terms of the z variable to the left side, and the terms of the t variable to the right side of the equality. Simplify the expression \frac{1}{e^{-z}}dz. Integrate both sides of the differential equation, the left side with respect to z, and the right side with respect to t.
Solve the differential equation dz/dt=-4e^(t-z)
Final answer to the exercise
$z=\ln\left(-4e^t+C_0\right)$