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Find the orthogonal trajectory of the curves 3x2y+2x3-y3-2y2 = ?, where &lpha is a constant
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3x2y+2x2y32y2=αDifferentiating this w.r.t x3(2xy+x2y)+4x3y2y4y y=0To find the orthogonal trajectory, replacing yby1y3(2xyx2y)+4x+3y2y+4yy=0

Multiplying throughout by y'3(2xyyx2)+4xy+3y2+4y=0 6xyy+4xy3x2+3y2+4y=0(6xy+4x) dydx 3x2+3y2+4y=0(6xy+4x) dy+(3x2+3y2+4y)dx=0

$\textit{Hence the Differential equation is …

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