Question

найти общее решение y"'=cos5x

Answer 1

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