2. Verify that the given differential equations are exact and solve the equations: (a) (4x³y - 15x² - y) dx + (x² + 3y² − x) dy = 0. (b) (tan(x) sin(x) sin(y)) dr + cos(x) cos(y)dy = 0.

Q: Solve the separable differential equation Subject to the initial condition: y(0) = 9. y = 11x -…

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Q: Solve the exact differential equation: (2y sin x cos x – y + 2y?e*y)dx = (x – sin? x – 4xye*y')dy

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Q: Verify that the given function y = sin (x2 + C ) is a solution of the given differential equation:…

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Q: Verify that the function y = x sin(x) + x cos(x) is a solution to the differential equation: y" + y…

A: 1 have verified the differential equation by finding each derivatives

Q: y(x) = C₁ + C₂e²x cos(5x) + c3e²* sin(5x)

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Q: Solve the differential equation. dy y + 1 dx O In |x| – ? () = tan - ex - x + tan-'(x) = C In |x| –…

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Q: Show that w(t) =〈sin(3t + 4),sin(3t − 2)〉, cos 3t satisfies the differential equation w''(t) =…

A: Given- wt=<sin3t+4,sin3t-2>,cos3t To prove- That the above expression satisfies the…

Q: Find all general solutions of y'(t)=(t+1)(y(t)2-1). Leave the solution as the form y(t)= an…

A: Given data:     The given differential equation is: y’(t)=(t+1)(y(t)2-1).     The given differential…

Q: Find the implicit solution of the differential equation (1+sin(y))dx + (1+x cos(y))dy = 0.

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Q: Please solve the following differential equation: dy (e2x + 4) – y dx (х — у) (4х + у)dx — x(у —…

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Q: (2y sin(x) cos(x) – y + 2y e) dx = (x – sin (x) – 4xyey)dy.

A: the differential equation Mdx+Ndy=0 is exact when ∂M∂y=∂N∂x where M and N are functions of x and y…