Find the differential equation of x2a2-y2b2-1

Differentiating the given eq. we get, 2xa^2dx+2yb^2dy=0 #160; 2xa^2dx= 2yb^2dy #160; dydx= xb^2ya^2 #160; dydx+xb^2ya^2=0 ...

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Standard XII

Mathematics

Formation of a Differential Equation from a General Solution

Find the diff...

Question

Find the differential equation of $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

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Solution

Differentiating the given eq. we get,

$\frac{2 x}{a^{2}} d x + \frac{2 y}{b^{2}} d y = 0$

$⟹ \frac{2 x}{a^{2}} d x = - \frac{2 y}{b^{2}} d y$

$⟹ \frac{d y}{d x} = - \frac{x b^{2}}{y a^{2}}$

$⟹ \frac{d y}{d x} + \frac{x b^{2}}{y a^{2}} = 0$

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Find the differential equation of x2a2+y2b2=1

Differentiating the given eq. we get,2xa2dx+2yb2dy=0 ⟹2xa2dx=−2yb2dy ⟹dydx=−xb2ya2 ⟹dydx+xb2ya2=0

Find the differential equation of $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

Differentiating the given eq. we get,

$\frac{2 x}{a^{2}} d x + \frac{2 y}{b^{2}} d y = 0$

$⟹ \frac{2 x}{a^{2}} d x = - \frac{2 y}{b^{2}} d y$

$⟹ \frac{d y}{d x} = - \frac{x b^{2}}{y a^{2}}$

$⟹ \frac{d y}{d x} + \frac{x b^{2}}{y a^{2}} = 0$