Question

Y'-3y/x=2x^4!!!!!! Срочно!!!!!! Пожалуйста!!!!! Баллами не обижу!!!!!!

Answer 1

$y'-\frac{3y}{x}=2x^4\\\\y=uv\; ,\; \; y'=u'v+uv'\\\\u'v+uv'- \frac{3uv}{x}=2x^4\\\\u'v+u(v'- \frac{3v}{x} )=2x^4 \\\\a)\; \; \frac{dv}{dx}- \frac{3v}{x}=0\; ,\; \; \; \int \frac{dv}{v} = 3\int \frac{dx}{x} \\\\ln|v|=3\, ln|x|\\\\v=x^{3}\\\\b)\; \; u'\cdot x^3=2x^4\\\\ \frac{du}{dx}=2x\\\\\int du=2\, \int x\, dx\\\\ u=2\cdot \frac{x^2}{2}+C=x^2+C\\\\c)\; \; \; y=x^3(x^2+C)$