Question

Solution of
dy /dx +y/x = logx
.​

Answer 1

Answer:

y = x/2(logx - 1/2) + C

Step-by-step explanation:

Differential Equation

dy/dx + y/x = logx

I. F. = e^(Integration Symbol(1/x)dx)

= e^(logex)

= x

Multiplying by Integrating factor

x(dy/dx) + y = xlogx

Integrating with respect to x

y.x = Integration Symbol (x.logx dx)

xy = logx. x^2/2 - Integration Symbol ((x^2/2)(1/x)dx)

xy = x^2 logx/2 - (1/2) (x^2/2) + C

y = x/2(logx - 1/2) + C

Answer 2

Answer is given in the pic.