Find k such that the given differential equation is exact (y + kzy – 2x)dr + (3ry² + 20z²y*)dy = 0

Determine whether the following ordinary differential equation cosh (3/y) - In(7y)y" = 11cos(4yx) - y³y¹ + 9x is linear or nonlinear by matching it with the differential equation an(x) dry dxn -+an-1(x) an-ly. + dxn-1 + a₁(x)- + ao(x)y= g(x) dx dy Linear Nonlinear

Solve the differential equation by Frobenius method with coefficients represented up to and including x3 dy -x- dx² dx 2x2d²y - - + (x²+1)y=0