Answer to Question #140046 in Differential Equations for Askin

Question

xy'=6y

Answer 1

$x \cdot y'=6y \\ y'=\frac{6y}{x} \\ \frac{y'}{y}=\frac{6}{x} \\ \frac{dy}{y}=\frac{6dx}{x} \\ \int \frac{dy}{y}=\int \frac{6dx}{x} \\ \ln|y|=6\cdot ln|x|+C_1 \\ \ln |y|=\ln x^6 +\ln C \\ y=C \cdot x^6$