Find the particular solution of the given differential equation

Question

dydx=−4xe(y−x^2);y=11whenx=1.

THanks

Answer 1

sarah, I am not certain what you meant to type.

i get this

dy/dx= -4x * e^ what is the exponent of e?

Answer 2

the exponent is (y-x^2)

Answer 3

dy/dx=−4xe^(y−x^2)
dy/dx = -4xe^y e^(-x^2)
-e^-y dy = 4x e^(-x^2)
e^-y = c-2e^(-x^2)
y = -ln(c - 2e^(-x^2))

since y(1) = 11,

-ln(c-2e^-1) = 11
c - 2e^-1 = e^-11
c = 2e^-1 + e^-11