Question

Solve the differential equation below, given the initial condition f(0) = 3. Express your answer using words or symbols. y=-5x^2

Answer 1

wheres the DE

Answer 2

the derivative is y'=-5x^2 my bad..

Answer 3

\[\large{\frac{dy}{dx}=-5x^2}\]\[\large{dy=-5x^2dx}\]now integrate both sides\[\large{y=\frac{-5x^3}{3}+C}\]

Answer 4

y(0)=3
\[\large{3=\frac{-5(0)}{3}+C}\] C=3

so\[y=\frac{-5x^3}{3}+3\]

Answer 5

thanks!!!

Answer 6

f(x) = y
f(0) is your x intercept