How do you solve the differential equation dy/dx=6y^2x, where y(1)=1/25 ?

ecoanuncios7x 2022-09-27 Answered
How do you solve the differential equation d y d x = 6 y 2 x , where y ( 1 ) = 1 25 ?
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Answers (1)

cisalislewagobc
Answered 2022-09-28 Author has 8 answers
d y d x = 6 y 2 x
Separate the variables:
1 y 2 d y = 6 x d x
Integrate both sides:
1 y 2 d y = 6 x d x
- 1 y = 3 x 2 + C
1 y = - 3 x 2 + C
y = - 1 3 x 2 + C
where C is an arbitrary constant of integration.
Now solve for y(1) to find C:
y ( 1 ) = 1 25 = - 1 3 ( 1 ) 2 + C
- 1 25 = 1 3 + C
3 + C = - 25
C = - 28
Hence, the final solution is:
y = - 1 3 x 2 - 28
y = 1 28 - 3 x 2
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