Exercise
$u'=5e^{8x-u}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation u^'=5e^(8x-u). Rewrite the differential equation using Leibniz notation. 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 u variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{1}{e^{-u}}du.
Solve the differential equation u^'=5e^(8x-u)
Final answer to the exercise
$u=\ln\left(\frac{5e^{8x}+C_1}{8}\right)$