If (My - Nx) / N = Q, where Q is a function of x only, then the differential equation M + Ny' = 0 has an integrating factor of the form ?(x) = e^?Q(x) dx. Find an integrating factor and solve the given equation. (18x²y + 2xy + 6y³) dx + (x² + y²) dy = 0 The integrating factor is ?(x) = Do not enter an arbitary constant. The solution in implicit form is = c, where c is a constant of integration.

          If (My - Nx) / N = Q, where Q is a function of x only, then the differential equation M + Ny' = 0 has an integrating factor of the form ?(x) = e^?Q(x) dx. Find an integrating factor and solve the given equation. (18x²y + 2xy + 6y³) dx + (x² + y²) dy = 0
The integrating factor is ?(x) = 
Do not enter an arbitary constant. The solution in implicit form is = c, where c is a constant of integration.

If (My - Nx) / N = Q, where Q is a function of x only, then the differential equation M + Ny' = 0 has an integrating factor of the form ?(x) = e^?Q(x) dx. Find an integrating factor and solve the given equation. (18x²y + 2xy + 6y³) dx + (x² + y²) dy = 0
The integrating factor is ?(x) =
Do not enter an arbitary constant. The solution in implicit form is = c, where c is a constant of integration.

Added by Timothy J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

07/30/2023

Step 1

Now, we are given that the integrating factor p(x) is of the form e^(∫R(x) dx), where R(x) is a function of x only. We need to find R(x) such that: (Nx - My) / (Mx - Ny) = R(x) Taking the partial derivatives, we get: Nx = ∂N/∂x = 2x My = ∂M/∂y = 18xk + 2x + Show more…

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If (My-Nx)/N = Q, where Q is a function of x only, then the differential equation M + Ny' = 0 has an integrating factor of the form μ(x) = e^∡Q(x)dx. Find an integrating factor and solve the given equation. (18x²y + 2xy + 6y³) dx + (x² + y²) dy = 0 The integrating factor is μ(x) = Do not enter an arbitrary constant. The solution in implicit form is = c, where c is a constant of integration.