Question

please
Find the particular and general solution of the equations:

(1+x2)dy–2x(y+3)dx=0
y=–1, x=0

Answer 1

Answer:

solved

Step-by-step explanation:

(1+x2)dy–2x(y+3)dx=0

y = –1 , x = 0

(1+x²)dy–2x(y+3)dx=0

(1+x²)dy =2x(y+3)dx

dy/ (y+3) = 2xdx/ (1+x²)

∫dy/ (y+3) = ∫2xdx/ (1+x²)

ln ( y +3 ) = ln (1+x²) + ln A  , A = constant

ln ( y +3 ) = ln A(1+x²)

y + 3 = A(x² + 1)

y  = A(x² + 1) -3 , -1 = A -3 , A = 2

general solution         →  y  = A(x² + 1) -3

particular solution      →   y  = 2(x² + 1) -3