Question

найти общее решение y"'=cos5x

Answer 1

$y''' = cos(5x)\int {y'''(x)} , dx = y'' = frac{1}{5}sin(5x) + c_1\int {y''(x)} , dx = y' = -frac{1}{25}cos(5x) + c_1x + c_2\int {y'} , dx = y = -frac{1}{125}sin(5x) + c_1'x^2 + c_2x + c_3, quad (c_1' = c_1/2)$