Initial value problem through origin (dz)/(dt)=8t*e^z , Through the origin

Clara Dennis

Clara Dennis

Answered question

2022-11-11

Initial value problem through origin
d z d t = 8 t e z , Through the origin
I have never done an initial value problem before, but I took it to mean that it gave me the initial value of the differential equation (0, 0) and that I should find the general value of the differential equation from it. Please correct me if I am wrong about this.
I started off by separating the variables:
d z e z = 8 t d t
I then integrated:
e z = 4 t 2 + c
After dividing by -1 and taking the natural log I have:
z = l n ( 4 t 2 + c )
Here is where my problem is, no matter what I plug in for c I cannot get the function to equal 0 when t = 0. Even for another value of t it does not seem to possible to get 0 with this differential equation.

Answer & Explanation

hocelwsmjc

hocelwsmjc

Beginner2022-11-12Added 16 answers

You solved the ODE correctly. We have
z ( t ) = ln ( 4 t 2 + c ) z ( 0 ) = ln ( c ) ln ( c ) = 0 c = 1 ,
because ln 1 = 0. Ok?

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?