What is the solution for (dy)/(dx)+ln(x)y=3ln(x) ?

The solution for (dy)/(dx)+ln(x)y=3ln(x) is y=e^{x+c_{1}}x^{-x}+3

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(dy)/(dx)+ln(x)y=3ln(x)

\frac{d y}{d x} + ln (x) y = 3 ln (x)

y = e^{x + c_{1}} x^{- x} + 3

Solution steps

\frac{d y}{d x} + ln (x) y = 3 ln (x)

Solve separable ODE:

y = e^{x + c_{1}} x^{- x} + 3

y = e^{x + c_{1}} x^{- x} + 3

y^{^{'}} = 2 y^{- 2}, y (0) = 3

(y + 2) d x + 25 - x^{2} d y = 0

2 x^{2} y + 3 x y^{^{'}} - 15 y = 0

- 5 \frac{d y}{d x} = 2 y - 150

(ln (y))^{2} \frac{d y}{d x} = x^{2} y

What is the solution for (dy)/(dx)+ln(x)y=3ln(x) ?
The solution for (dy)/(dx)+ln(x)y=3ln(x) is y=e^{x+c_{1}}x^{-x}+3