4(a)Verify that the equation y = In x Iny is an implicit solution of the...

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4(a)Verify that the equation y = In x – Iny is an implicit solution of the IVP, ydx x(y + 1)dy y(e) = 1 [10marks] (b) Consider the IVP, test whether it is exact and solve it. x(х — у)dy %3D - (3ху — у?)dx У(-1) %3D 1 [9marks] (c) Determine the degree of the following homogeneous function (i) f (x, y) = 4x² + 2y*, [2marks] %3D (ii) f(x, y) = /5x6 – 3y6 + 4x²y4, [4marks] 4(a)Verify that the equation y = In x – Iny is an implicit solution of the IVP, ydx x(y + 1)dy y(e) = 1 [10marks] (b) Consider the IVP, test whether it is exact and solve it. x(х — у)dy %3D - (3ху — у?)dx У(-1) %3D 1 [9marks] (c) Determine the degree of the following homogeneous function (i) f (x, y) = 4x² + 2y*, [2marks] %3D (ii) f(x, y) = /5x6 – 3y6 + 4x²y4, [4marks]