Solve the given differential equation subject to the indicated initial condition. (1 + x^4) dy + x(1 + 4y^2) dx = 0, y(1)= 0

Damien Horton 2022-07-25 Answered
Solve the given differential equation subject to the indicated initial condition.
( 1 + x 4 ) d y + x ( 1 + 4 y 2 ) d x = 0 , y ( 1 ) = 0
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Answers (1)

ab8s1k28q
Answered 2022-07-26 Author has 17 answers
( 1 + x 4 ) d y + x ( 1 + 4 y 2 ) d x = 0 , y ( 1 ) = 0 separable diff.eqn
d y 1 + 4 y 2 = x d x 1 + x 4 integrate both sides
1 1 + 4 y 2 d y = x 1 + x 4 d x
1 1 + ( 2 y ) 2 d y = x 1 + x 4 d x
2y=v
2dy=dv
x=u
2xdx=du
1 2 arctan ( 2 y ) = 1 2 arctan ( x 2 ) + c
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