x=acosθ+bsinθand y=asinθ−bcosθ,show that y2dx2d2y−xdxdy+y=0

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{x}={a}{{}}+{b}{{}}and {y}={a}{{}}-{b}{{}},show that {y}^{{2}}

Question

$x = a cos θ + b sin θ$ and $y = a sin θ - b cos θ,$ show that $y^{2} \frac{d ^{2} y}{d x ^{2}} - x \frac{d y}{d x} + y = 0$

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x = a cos θ + b sin θ

and

y = a sin θ - b cos θ,

show that

y^{2} \frac{d ^{2} y}{d x ^{2}} - x \frac{d y}{d x} + y = 0

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Question Text

x = a cos θ + b sin θ

and

y = a sin θ - b cos θ,

show that

y^{2} \frac{d ^{2} y}{d x ^{2}} - x \frac{d y}{d x} + y = 0