| 2y | 2√y | |||
Proszę o pomoc w równaniu rózniczkowym bernulliniego y'+ | = | |||
| x | cos2x |
| 2y | 2√y | 1 | ||||
y' + | = | / * | ||||
| x | cos2(x) | √y |
| y' | 2√y | 2 | |||
+ | = | ||||
| √y | x | cos2(x) |
| 1 | ||
z = y1/2 ⇒ z' = | y−1/2y' | |
| 2 |
| 2z | 2 | |||
2z' + | = | |||
| x | cos2(x) |
| z | 1 | |||
z' + | = | |||
| x | cos2(x) |
| dz | z | ||
+ | = 0 | ||
| dx | x |
| dz | dx | ||
= − | |||
| z | x |
| C(x) | C'(x) | C(x) | ||||
z = | ⇒ z' = | − | ||||
| x | x | x2 |
| C'(x) | C(x) | C(x) | 1 | ||||
− | + | = | |||||
| x | x2 | x2 | cos2(x) |
| x | ||
C'(x) = | ||
| cos2(x) |
| x | ||
C(x) = ∫ | dx | |
| cos2(x) |
| 1 | ||
ale dlaczego się monoży przez | to jest niepotrzebne | |
| √y |
