Find a solution to Ordinary differential equation (d^2 z(x))/(dx^2)=b * e^((-a * z(x)))

racmanovcf

racmanovcf

Answered question

2022-10-15

Find a solution to ODE d 2 z ( x ) d x 2 = b e ( a z ( x ) )

Answer & Explanation

Layne Murillo

Layne Murillo

Beginner2022-10-16Added 14 answers

Hint:
d 2 z d x 2 = b e a z
d z d x d 2 z d x 2 = b e a z d z d x
d z d x d 2 z d x 2   d x = b e a z d z d x   d x
d z d x   d ( d z d x ) = b e a z   d z
1 2 ( d z d x ) 2 = b e a z a + c
( d z d x ) 2 = C 1 b e a z a
d z d x = ± C 1 b e a z a
Rene Nicholson

Rene Nicholson

Beginner2022-10-17Added 2 answers

0 e a z x e s x d x = 0 e x ( a z + s ) d x = e x ( a z + s ) a z + s | 0 = 1 a z + s

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