Question

Помогите решить пожалуйста!!!!

Answer 1

$- \frac{y(x)}{x} + y'(x) = x^{\frac{1}{3}}, \\ - \frac{y(x)}{x} + y'(x) = 0, \\ y'(x) = \frac{y(x)}{x}, \\ \frac{dy(x)}{y(x)} = \frac{dx}{x}, \\ \int {\frac{1}{y(x)}} \, dy(x) = \int {\frac{1}{x}} \, dx, \\ \ln y(x)= \ln x + \ln C, \\ y(x)=xC(x), \\ y'(x)=C(x)+xC'(x), \\ - \frac{xC(x)}{x} + C(x)+xC'(x) = x^{\frac{1}{3}}, \\ C'(x) = x^{-\frac{2}{3}}, \\ C(x) = \int {x^{-\frac{2}{3}}} \, dx = 3x^{\frac{1}{3}}+C_1, \\ y(x)= x(3x^{\frac{1}{3}}+C_1)=3x^{\frac{4}{3}}+C_1x$