What is a solution to the differential equation dy/dx=x+y?

Joyce Sharp

Joyce Sharp

Answered question

2022-09-18

What is a solution to the differential equation d y d x = x + y ?

Answer & Explanation

Nathalie Rivers

Nathalie Rivers

Beginner2022-09-19Added 7 answers

Let u=x+y
d u d x = d d x ( x + y ) = 1 + d y d x
d y d x = d u d x - 1
Thus, making the substitutions into our original equation,
d u d x - 1 = u
d u u + 1 = d x
d u u + 1 = d x
ln ( u + 1 ) = x + C 0
e ln ( u + 1 ) = e x + C 0
u + 1 = C 1 e x (where C 1 = e C 0 )
Substituting x+y=u back in,
x + y + 1 = C 1 e x
y = C 1 e x - x - 1

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