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Erkli o‘zgaruvchi, noma’lum funksiya va uning hosilalarini (differensiallarini) bog‘lovchi tenglamaga … deyiladi.
Differensial tenglama
Quyida berilganlardan differensial tenglamani toping. 1)x+y+8=0 2)xdx-ydy=0 3)xdx+3ydy-4=0 4)x-y2 -3=0
2
Birinchi tartibli oddiy differensial tenglamaning umumiy ko‘rinishini toping.
F(x,y,y')=0
2xy2dx-dy=0 differensial tenglamaning yechimini toping
y=-1/x2
Ushbu M(x)dx+N(y)dy=0 ko’rinishdagi differensial tenglamaga … differensial tenglama deyiladi.
o'zgaruvchilari ajralgan
xdx+ydy=0 differensial tenglamaning yechimini toping
x2 + y2 =C
2xdx- (3 y2 +1)dy=0
x2 - y3-y=C
xyy'=1- x2 differensial tenglamaning yechimini toping
x2/2 - ln|x|+y2/2=C
O'zgaruvchilari ajralgan differensial tenglamani toping 1) xydx-dy=0 2) xdx-ydy=0 3) dx+xydy=0 4) ydx+xdy
2
O'zgaruvchilari ajraladigan differensial tenglamani toping 1)(x+y)dx-dy=0 2) (x+y)dy 3) dx++xydy 4) ydx+(xydy
3
xdx+ydy=0 differensial tenglamaning yechimini toping
x^2+y^2=C
xyy'=1-x^2 differensial tenglamaning yechimini toping
x^2/2-ln|x|+y^2/2=C
