find the general solution of the differential equation.\n$\frac{dy}{dx}=\frac{10}{x}$\n$y=square$\n(use…

find the general solution of the differential equation.\n$\frac{dy}{dx}=\frac{10}{x}$\n$y=square$\n(use parentheses to clearly denote the argument of each function.)

find the general solution of the differential equation.\n$\frac{dy}{dx}=\frac{10}{x}$\n$y=square$\n(use parentheses to clearly denote the argument of each function.)

Answer

Explanation:

Step1: Separate variables

Separate (y) and (x) terms. We get (dy = \frac{10}{x}dx).

Step2: Integrate both sides

Integrate (\int dy=\int\frac{10}{x}dx). The integral of (dy) is (y), and the integral of (\frac{10}{x}dx) is (10\int\frac{1}{x}dx). Since (\int\frac{1}{x}dx=\ln|x| + C), then (10\int\frac{1}{x}dx = 10\ln|x|+C).

Answer:

(y = 10\ln|x|+C)