Solve the Equation: (dy)/(dx)=1/(x+y^2)

ferdysy9

ferdysy9

Answered question

2022-08-08

Solve the Equation:
d y d x = 1 x + y 2

Answer & Explanation

Alisa Medina

Alisa Medina

Beginner2022-08-09Added 4 answers

d y d x = 1 x + y 2
d x d y = x + y 2
d x d y x = y 2 ...(1)
This is a linear equation of first order in x
where P ( y ) = 1 , Q ( y ) = y 2
Now P d y = d y = y
I . F = e P d y = e y
The general solution of (1) is
x e y = y 2 e y d y
= y 2 e y d y 2 y e y d y
= y 2 e y 2 y e y d y
= y 2 e y 2 ( y e y e y d y )
x e y = y 2 e y + 2 y e y 2 e y + C
x = y 2 + 2 y 2 + C e y
x + y 2 2 y + 2 = C e y

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