solve the following first-order differential equations by first finding the integrating factor: (2x+tany) + (x-x^2 tany) dy/dx = 0. This is an exact differential equation.

Question 4. The Fourier series representation, FS(t), of a function f(t), where f(t + 8) = f(t) is given by nπt FS(t) = 4+ [a, cos(xt) - Σ 2 4 n=1 an In this particular case the Fourier series coeffcients are given by ao 1 bn = = = 3(-1)" Nπ + bn sin 3(1-2(−1)n) n²π² nπt 4 Compute the Fourier series coefficients for n = 1, 2, 3 correct to 4 decimal places and hence, using these entered values, compute FS3 (2) correct to decimal places. Enter the values in the boxes below. Enter a₁ correct to 4 decimal places: Enter a correct to 4 decimal places: Enter a correct to 4 decimal places: Enter b₁ correct to 4 decimal places: Enter b₂ correct to 4 decimal places: Enter b3 correct to 4 decimal places: Enter FS3 (2) correct to 3 decimal places:

solve this differential equation using reduction of order (2nd order)

dy + 4y = t cos 2t dt? Solve the differential equation