Question

Solve for Bernoulli given
y'=2(3x+y)^2-1

Answer 1

Step-by-step explanation:

It is a Bernoulli equation with P(x)=x5, Q(x)=x5, and n=7, let's try the substitution:

u = y1−n

u = y−6

In terms of y that is:

y = u(− 16 )

Differentiate y with respect to x:

dydx = −16 u(− 76 ) dudx

Substitute dydx and y into the original equation dydx + x5 y = x5 y7

−16 u( −76 ) dudx + x5u( −16 ) = x5u( −76 )

Multiply all terms by −6u( 76 )

dudx − 6x5u = −6x5