how can I solve the separable differential equation?

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how can I solve the separable differential equation?

how can I solve the separable differential equation
ydx - (1+x)dy = 0
can you explain me step by step?

2007-02-26 06:07:36 · 1 answers · asked by azulita 3 in Science & Mathematics ➔ Engineering

1 answers

ydx - (1+x)dy = 0
ydx = (1+x)dy
dy/y = dx/(1+x)
ln(y) = ln(1 + x) + ln(C)
y = C(x + 1)

dy/dx = C
but C = y/(1 + x)
dy/dx = y/(1 + x)
(1 + x)dy = ydx
0 = ydx - (1 + x)dy

2007-02-26 06:22:44 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋