Solve differential equations by using integrating factors

Question

1. (dr/dθ)+rcotθ=sinθ
2. y+x(x-1)(dy/dx)=x³e^{-x^2}
3. x(dy/dx)=y+x²(sin+xcosx) and y = 0 when x = π/2
4. dy/dx = x - xy and y = 0 when x = 0

Answer 1

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