1. Solve the following differential equations and find particular solutions where possible. Where the differential equation...

 

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1. Solve the following differential equations and find particular solutions where possible. Where the differential equation is exact, show why you say it is exact. Show all your work. 1. x?(y+ 1)dx = y?(1- x)dy 2. dy sinx – y tanx dx 3. 2y = (x3 + xy?) %3D dx 4. x- x²y2 +y = 0 dx 5. (sec?x coty - y)dx (tanx cosec?y + x)dy 0 x2 dy = y? - xy 6. y(1) = 1 QUESTION 2: 1. Show that the solution of: dy x y 1.1 with initial condition, y(1) = 2 dx 1+x3 1. Solve the following differential equations and find particular solutions where possible. Where the differential equation is exact, show why you say it is exact. Show all your work. 1. x?(y+ 1)dx = y?(1- x)dy 2. dy sinx – y tanx dx 3. 2y = (x3 + xy?) %3D dx 4. x- x²y2 +y = 0 dx 5. (sec?x coty - y)dx (tanx cosec?y + x)dy 0 x2 dy = y? - xy 6. y(1) = 1 QUESTION 2: 1. Show that the solution of: dy x y 1.1 with initial condition, y(1) = 2 dx 1+x3

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