What is the solution for x(dy)/(dx)+2y=sin(x) ?

The solution for x(dy)/(dx)+2y=sin(x) is y=-(cos(x))/x+(sin(x))/(x^2)+(c_{1})/(x^2)

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x(dy)/(dx)+2y=sin(x)

x \frac{d y}{d x} + 2 y = sin (x)

y = - \frac{cos ( x )}{x} + \frac{sin ( x )}{x ^{2}} + \frac{c _{1}}{x ^{2}}

Solution steps

x \frac{d y}{d x} + 2 y = sin (x)

Solve linear ODE:

y = - \frac{cos ( x )}{x} + \frac{sin ( x )}{x ^{2}} + \frac{c _{1}}{x ^{2}}

y = - \frac{cos ( x )}{x} + \frac{sin ( x )}{x ^{2}} + \frac{c _{1}}{x ^{2}}

\int \frac{e ^{8 x}}{x} d x

x \to 0 lim (csc^{2} (x))

\int \frac{sin ( 21 x )}{1 + cos ^{2} ( 21 x )} d x

\int_{0}^{1} x (1 - x) d x

6 x^{2}, x^{2} + 8

What is the solution for x(dy)/(dx)+2y=sin(x) ?
The solution for x(dy)/(dx)+2y=sin(x) is y=-(cos(x))/x+(sin(x))/(x^2)+(c_{1})/(x^2)