róż2

RÓWNANIA RÓŻNICZKOWE ZWYCZAJNE RZĘDU I - ZADANIA
	Rozwiąż równanie:
1. xdx + (y + \)dy = 0	2.	x dx + ydy = 0
3. xdy + ydx = 0	4.	*(1 + y^2 )dx + y(l + x^2 )dy = 0
5. (xy-x)dx + (xy + x-y-\)dy~0	6.	(x + 2x^3 )dx + (y + 2y )dy = 0
7. y.'-' X + 1	8.
9. (J7^2 + xy^2 )dx + (X^2 - yx^2 )dy = 0	10.	(1 - x)dy -ydx = 0. y0 = l,x0 = 0
11. dx-yj\-x^2dy = 0, y0=^,x0 = 1	12.	y = jcosx, yo) = i
13. ^dy=^x+ydx x	14.	dy x + y dx x -y
15. (x^2 + 2xy-y^2)dx + (y^2 + 2xy-x^2)dy = 0	16.	xy' = 3y-2x-2yjxy-x^2, y{ 1) = 2
17. y' + -y = 3x X	18.	xdy + (a-^2 - y)dx = 0
19. y~^sin;c = sin;rcos;c	20.	(l + x^2)y'-2xy = (l + x^2)^2
21. ydx + 2(x + y)dy = 0	22.	(x - 2xy - y^2 )y' + y^2 -0
23. y'--y = x X	24.	y' + 2xy = 2xe~^x
25. y' + y- 2e^x	26.	y' + xy = x^2 + 1
, \ + 2x \ + 2x ^27• y 2 y^= 2 + x * + ;c	28.	y' + -y=-y(l) = l X X
29. xy' = x + ^y, y(0) = 0	30.	y' - 2xy = 2x^3y^2
31. y' + -±Ty = xfi 1 -X	32.	, 1 1 y —y=^~ x 2 y
33. (xy + x^2y^3)y’ = 1	34.	y' + 2xy - 2x^3y^3
35. xy' + y = y^2\nx, y(l) = l	36.	3 y^2y'+y^i +* = o
2 37. y - 9*^2jy = ^5 +x^2jy^3, y(0) = 0	38.	y'-y = xy^2, y(0) = 0
39. xy'-y = y^2, j(0) = 0	40.	xy' + y = xy^2, y0) = 0
41. xJy^2 +1 +yyjx^2 +1^- = 0, j(0) = l dx	42.	7 dy 2 2 x — = x +xy + y dx
x^3-3 x^2y + xy^2-y^3 y y^3 + 2xy^2	44.	Jx^4 +y^4 -2xyy' = x^x^2 +y^2
.. dy cosx y 45. —---.—^arctgjc = -r—2—<r- dx vsin x + 1 jarctg*	46.	y' + xy = .r sin x^2
47. y' + y + y^2 sin;c = 0	48.	y' + y + xjy = 0