Solve the differential equation $(1 + 3x - 6y)dx + (2x - 4y - 2)dy = 0$ by multiplying it by an \"integrating factor\" $e^{ax + by}$ so that the resulting equation $e^{ax + by}(1 + 3x - 6y)dx + e^{ax + by}(2x - 4y - 2)dy = 0$ is exact. Find the required constants $a$ and $b$, and then find the general solution in implicit form $f(x, y) = $ const.

          Solve the differential equation
$(1 + 3x - 6y)dx + (2x - 4y - 2)dy = 0$
by multiplying it by an \"integrating factor\" $e^{ax + by}$ so that the resulting equation
$e^{ax + by}(1 + 3x - 6y)dx + e^{ax + by}(2x - 4y - 2)dy = 0$
is exact.
Find the required constants $a$ and $b$, and then find the general solution in implicit form $f(x, y) = $ const.

Solve the differential equation
(1 + 3x - 6y)dx + (2x - 4y - 2)dy = 0
by multiplying it by an ïntegrating factor$̈e^ax + byso that the resulting equatione^ax + by(1 + 3x - 6y)dx + e^ax + by(2x - 4y - 2)dy = 0is exact.
Find the required constantsaandb, and then find the general solution in implicit formf(x, y) = const.

Added by Lori D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Keondre Parker

Step 1

Given equation: (1+3x -6y)dx+(2x-4y-2)dy=0 Partial derivative of (1+3x -6y) with respect to y: -6 Partial derivative of (2x-4y-2) with respect to x: 2 Since the partial derivatives are not equal, the given differential equation is not exact. Show more…

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Solve the differential equation (1+3x -6y)dx+(2x-4y-2)dy=0. 0=fip(Z-fip-IZ)nq+rp2+xp(fi9-Tg+1)riq+zo3 is exact. Find the required constants a and b, and then find the general solution in implicit form f(x, y) = const.