Differential Eqn and Advance Math

Find the differential equation of the family of lines passing through the origin

• ydx - xdy = 0

• xdy - ydx = 0

• xdx + ydy = 0

• ydx + xdy = 0

What is the differential equation describing the family of parabolas having their vertices at the origin and their foci on the x-axis?

• 2xdy-ydx=0

• xdy + ydx = 0

• 2ydx - xdy = 0

• dy/dx - x =0

Determine the differential equation describing the family of line passing through (h, k).

• (y-k)dx - (x-h)dy =0

• (y-h) + (y-k)= dy/dx

• (x - h)dx - (y - k)dy = 0

• (x + h)dx - (y- k)dy = 0

• -xe^-x + lny = C

• -xe^-x+1 + lny = C

• -(x + 1)e^-x +lny= C

• -(x + 1)e^-x+1 + lny = C

• x/y = lnx + C

• y = x/2lnx + c

• y = 1/ln x + c

• y/x = lnx + c

• y²x - 3xy = C

• y²x+3xy=C

• x²y + 3xy = C

• x²y - 3xy = C

Find the general solution to the differential equation, (2xy + 3y)dx + (x² + 3x)dy = 0

• x²y + 3xy = C

• xy + 3x²y = C

• xy +x²y = C

• 3xy + 3x²y = C

• yx² -(1/3)x² = C

• yx² +(1/3)x² = C

• yx² -(1/4)x² = C

• yx² +(1/4)x² = C

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Find the general solution to differential equation,

(y² - x²)dx-2xydy = 0

• x²+ y² = Cx

• x²- y² = Cx

• -x²- y² = Cx

• -x²+ y² = Cx