tentukan penyelesaian persamaan diferensial dari 3x2(y-1)2 dx+2x3(y-1) dy = dimana y (-2)= 3.5

3x²(y-1)² dx + 2x³(y-1) dy = 0
3x²(y-1)² dx = -2x³(y-1) dy
(3x²)/(2x³) dx = -(y-1)/(y-1)² dy
(3/2)(1/x) dx = -1/(y-1) dy
∫(3/2)(1/x) dx = -1/(y-1) dy
(3/2)lnx = -ln(y-1) + lnc
lnx^(3/2) = ln(c/(y-1))
x^(3/2) = c/(y-1)
(y-1).x^(3/2) = c
(y-1) = c/(x^(3/2))
y = c/(x^(3/2)) + 1

y(-2) = 7/2

c/((-2)^(3/2)) + 1 = 7/2
ci/(√8) = 7/2 - 1
ci/(√8) = 5/2
c = (5/2)(√8/i)
c = (5/2)(2√2/ii)
c = 5√2/i
c = 5√2i/(-1)
c = -5√2 i

y(x) = -(5√2 i)/(x^(3/2)) + 1