Find the solution to the differential equation dz/dt = 7te^4z that passes through the origin.

Step-by-step explanation:

from the equation, .

we can give different approach to the equation, but to make it simple and direct, let separate the equation by bringing all like terms to the same side i.e

.

if we integrate both side,

since the equation passes through the origin, and at the origin z=0 and t=0

we substitute this values and solve for the constant c

.

If we substitute the value of c into the equation we arrive at

if we the the natural logarithm of both sides, we arrive at

answer: 34rtyj,jkhtyetwrhyjeuiejnbhdfknbkguxfrbhkfdbjvkmbd,kvbsd.kxjvbhjnfbgjxdfn

step-by-step explanation:

step-by-step explanation: