y"+y=sin(x)+ (x)cos(x)?

Question

Encuentre un Yp particular de la solución de la ecuación dada

Answer 1

y" + y = 1

1=sin(x) + xcos(x)

Equation should read 1=sin^2(x) + xcos^2(x)
and x value is elements of real numbers.

Answer 2

y(x) = Ao + A1 x + A2 x^2 + A3 x^3 + A4 x^4 + ....

y''(x) = 2 A2 + 6 A3 x + 12 A4 x^2 + ....

sin(x) = x - (x^3 / 3!) + (x^5 / 5!) - (x^7 / 7!) + (x^9 / 9!) -....

x cos(x) = x - (x^3 / 2!) + (x^5 / 4!) - (x^7 / 6!) + ....

Add each side and equate coefficients to get the particular solution.

Answer 3

note that Y" usually means the antiderivative of the second derivative of y. ie Y"=y'