State an existence theorem for the differential equation -, Mathematics

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State an existence theorem for the differential equation -

(a) State an existence theorem for the differential equation, dy/dx= f(x,y), y(x₀) = y₀

(b) Using Picard's method of successive approximation, Solve the differential equation, dy/dx =y+ cos(2x), y(0)=2,

Find y0, y1, y2 after converting it to an integral equation

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