What is a solution to the differential equation dy/dt=e^t(y−1)^2?

sailorlyts14eh 2022-09-29 Answered
What is a solution to the differential equation d y d t = e t ( y - 1 ) 2 ?
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Answers (1)

blikath3
Answered 2022-09-30 Author has 7 answers
We have:
d y d t = e t ( y - 1 ) 2
We can collect terms for similar variables:
1 ( y - 1 ) 2   d y d t = e t
Which is a separable First Order Ordinary non-linear Differential Equation, so we can "separate the variables" to get:
  1 ( y - 1 ) 2   d y = e t   d t
Both integrals are those of standard functions, so we can use that knowledge to directly integrate:
- 1 y - 1 = e t + C
And we can readily rearrange for y:
- ( y - 1 ) = 1 e t + C
1 - y = 1 e t + C
Leading to the General Solution:
y = 1 - 1 e t + C
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