Question

Помогите срочно пожалуйста

Answer 1

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

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