| 3x+y | ||
y' = | y(1)=0 | |
| x−3y |
| 3x+y | 3+(y/x) | |||
y' = | = | |||
| x−3y | 1−3(y/x) |
| y | ||
Podstawienie u = | , wtedy y = ux skąd y' = u + xu' | |
| x |
| 3+u | ||
u + xu' = | ||
| 1−3u |
| 1+u2 | ||
xu' = 3* | ||
| 1−3u |
| 1−3u | 3 | ||
du = | dx | ||
| 1+u2 | x |
| 3 | ||
arctan(u) − | ln(1+u2) = 3ln|x| + C | |
| 2 |
| y(1) | ||
y(1) = 0 ⇒ u(1) = | = 0 ⇒ 0 = 0 + C. | |
| 1 |
| y | y2 | |||
2arctan( | ) − 3ln(1+ | ) = 6ln|x|. | ||
| x | x2 |