Question

Solve the general solution of the equation [ x + sin(y/x) ] dx - x sin(y/x) dy = 0​

Answer 1

Answer:

cos(y/x) + logx = c

Step-by-step explanation:

[ x + sin(y/x) ] dx - x sin(y/x) dy = 0

==> [ 1 + (y/x) sin (y/x) ] = sin (y/x)dy/dx

Let y = vx

dy/dx = (v + x)dv/dx

1 + v • sin x / sin v = (v + x)dv/dx

==> 1/sin v + v = (v + x)dv/dx

1/sin v = (x)dv/dx

Integrate both sides, we get

dx/x = sin v dv + c

logx = -cos v + c

==> cos(y/x) + logx = c

Answer 2

Answer:

cos(y/x) + logx = c

Step-by-step explanation:

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