Solve the initial value problem given by the differential equation dydx=x6y2 together with the initial condition: if x=−3 then y=4 . To solve this, rearrange and integrate to get
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To solve the separable differential equation we must find two separate integrals: dy = and dx = The first integral we integrate by substitution: u = du = Solving for y we get one positive solution y = and one negative solution y = (Note: you must simplify all arbitrary constants down to one constant k) Find the particular solution satisfying the initial condition y(1) = -6. y(x) =
Adi S.
Solve the given differential equation. $$x^{-3} d y=4 y d x, y(0)=3$$
Integral Calculus
Differential equations (Optional)
To solve the separable differential equation, we must find two separate integrals: ∫ 2y/(y^2-6) dy and ∫ 1/(x^2) dx. The first integral can be solved by substitution: u = y^2 - 6, du = 2y dy. Solving for y, we get one positive solution y = sqrt(ke^(-1/x)+6) and one negative solution y = -sqrt(ke^(-1/x)+6) (Note: you must simplify all arbitrary constants down to one constant k). Find the particular solution satisfying the initial condition y(1) = -8.
Melissa M.
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