For each of the following differential equations, determine whether it is an exact equation or not. If it is, calculate a general solution; if it is not, state that the method of exact equations does not apply. (2+7² - y²) dx + (1²-2 (y² - 2xy + 24-²y) d 3 b. (2xy - 3y) dx + (−6x+3y + 2x²) dy = 0 a. dy = 0 When solved for the derivative, assuming y0, each of the equations a and b is equivalent to the following first-order ODE: dy dx -2xy + 3y 2x² - 6x + 3y Nonetheless, applying the method of exact equations yields different results!

Q: Covert the differential equation into a system and solve the system: D2-2D+3y=0

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Q: Test whether the differential equation is exact: (e2y – ycosxy)dx + (2xe2y – xcosxy+ 2y)dy = 0 Find…

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Q: Covert the differential equation into a system and solve the system: D2-2D-8y

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Q: 18.Find the general solution of the differential equation %3D xp xy-y2

A: To solve the given differential equation, first we convert it into separable form, and then we find…

Q: (x - 2 y – 6) dæ + (2 x + y + 8) dy = 0

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Q: dy Q-2. Solve the differential equation by direct method dr 1³ + 9x² + 27x+ 27

A: Given differential equation dydx=1x3+9x2+27x+27 It can be written as dydx=1x+33 ⇒dy=1x+33dx…

Q: (x²y³ + y + cos(2x)) dx + (x³y² + x +e³y)dy = 0

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Q: Determine the type of DE/method of solution to be used and solve. y′ = x3 − 2xy, when x = 1 and y =…

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Q: (22 + y? +1) dæ + x (x – 2y) dy = 0

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Q: Solve each of the following: (x − y − 2)dx + (3x + y - 10)dx = 0

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Q: Solve for the Linear Equations y′=x−2y

A: y'=x-2y⇒y'+2y=x Now comparing with y'+Py=Q, we get P=2  &  Q=x Now integrating factor is,…

Q: Use the method of comparing the coefficients to find a particular solution for the differential…

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Q: Verify that the given differential equation is exact; then solve it. 2 (9x² +6y²) dx + (12xy + 12y²)…

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Q: Solve the exact equation (6xy - y³ )dx + (4y +3x² − 3xy 2 )dy = 0

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