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Differential Equations Ncert Solutions Maths class 12th Maths Class 12th Differential Equations

103. Find the equation of the curve passing through the point (0,π/4), whose differential equation is sin x cos y dx + cos x sin y dy = 0.

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Vishal Baghel | Contributor-Level 10

4 months ago

The differential equation of the given curve is:

$\begin{array}{l} s i n x c o s y d x + c o s x s i n y d y = 0 \\ \Rightarrow \frac{s i n x c o s y d x + c o s x s i n y d y}{c o s x c o s y} = 0 \\ \Rightarrow t a n x d x + t a n y d y = 0 \end{array}$

Integrating both sides, we get:

$\begin{array}{l} l o g (s e c x) + l o g (s e c y) = l o g C \\ l o g (s e c x . s e c y) = l o g C \\ \Rightarrow s e c x . s e c y = C . . . . . . . . . . (1) \end{array}$

The curve passes through point $(0, \frac{π}{4})$

$\begin{array}{l} ∴ 1 \times\sqrt2 = C \\ \Rightarrow C =\sqrt2 \end{array}$

On subtracting $C =\sqrt2$ in equation (10, we get:

$\begin{array}{l} s e c x . s e c y =\sqrt2 \\ \Rightarrow s e c x . \frac{1}{c o s y} =\sqrt2 \\ \Rightarrow c o s y = s e c x/√2 \end{array}$

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103. Find the equation of the curve passing through the point (0,π/4), whose differential equation is sin x cos y dx + cos x sin y dy = 0.

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