Question

Срочно решите задачу x^3*y''+x^2*y'=1​

Answer 1

$x^3y''+x^2y'=1\ \ xy''+y'=dfrac{1}{x^2}\ \ Big(xy'Big)'=dfrac{1}{x^2}\ \ \ displaystyle xy'=int dfrac{dx}{x^2}=-dfrac{1}{x}+C_1\ \ y'=-dfrac{1}{x^2}+dfrac{C_1}{x}\ \ y=int left(-dfrac{1}{x^2}+dfrac{C_1}{x}right)dx=dfrac{1}{x}+C_1ln |x|+C_2$