Question

Помогите срочно пожалуйста

Answer 1

$y'+dfrac{y}{x}=2x^3\ xy'+y=2x^4\ (xy)'_x=2x^4\ xy=int 2x^4 dx\ xy=dfrac{2x^5}{5}+C\ y=dfrac{2x^4}{5}+dfrac{C}{x}$

$y''-3y'+2y=5e^{3x}\ lambda^2-3lambda+2=0=>lambda=2;;;;;lambda=1=>y_{oo}=C_1e^{2x}+C_2e^x\ left [ y=Ce^{3x}right ]\ 9Ce^{3x}-9Ce^{3x}+2Ce^{3x}=5e^{3x}=>C=dfrac{5}{2}=>y_{r_H}=dfrac{5}{2}e^{3x}\ y=dfrac{5}{2}e^{3x}+C_1e^{2x}+C_2e^x$