Question

y""=x²+1 математика помогите пожалуйста ​

Answer 1

Пошаговое объяснение:

$y''''=x^2+1\\ y'''= \int( {x}^{2} + 1)dx = \int{x}^{2}dx + \int 1dx \\ y'''= \frac{ {x}^{3} }{3} + x + C$

$y'' = \int(\frac{ {x}^{3} }{3} + x + C )dx = \\ = \int\frac{ {x}^{3} }{3} dx + \int xdx + \int C dx \\ y'' = \frac{ {x}^{4} }{12} + \frac{ {x}^{2} }{2} + Cx+D$

$y' = \int(\frac{ {x}^{4} }{12} + \frac{ {x}^{2} }{2} + Cx+D)dx = \\ = \frac{ {x}^{5} }{12 \times 5} + \frac{ {x}^{3} }{2 \times 3} + \frac{Cx^{2}}{2} +Dx + E \\ y' = \frac{ {x}^{5} }{60} + \frac{ {x}^{3} }{6} + \frac{Cx^{2}}{2} +Dx + E$

$y= \int(\frac{ {x}^{5} }{60} + \frac{ {x}^{3} }{6} + \frac{Cx^{2}}{2} +Dx + E)dx = \\ = \tfrac{ {x}^{6} }{6 \cdot60} + \tfrac{ {x}^{4} }{6\cdot4} + \tfrac{Cx^{3}}{2\cdot3} + \tfrac{Dx^{2}}{2} + Ex + F = \\ = \frac{ {x}^{6} }{360} + \frac{ {x}^{4} }{24} + \frac{Cx^{3}}{6} + \frac{Dx^{2}}{2} + Ex + F; \: \\C, \: D, \: E, \: F \in \R$