Let C 1 and C 2 be two curves which satisfy the differential equation 2 dy - dx 2- x dy - dx - y and passes through 1-1- If the area enclosed by the curves C 1- C 2 and the axis is m - R then m - n -

Dy/dx= x ±√(x^2+8y)/4⇒ x=2y 1 and x+y=2 ∴ Area=5/4= m/n ...

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Byju's Answer

Standard XII

Mathematics

Solving Homogeneous Differential Equations

Let C 1 and C...

Question

Let $C_{1}$ and $C_{2}$ be two curves which satisfy the differential equation $2 {(\frac{d y}{d x})}^{2} + x (\frac{d y}{d x}) = y$ and passes through
(1, 1). If the area enclosed by the curves $C_{1}, C_{2}$ and the axis is $\frac{m}{R}$ then m+n=___

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Solution

$\frac{d y}{d x} = \frac{- x \pm \sqrt{x^{2} + 8 y}}{4} \Rightarrow x = 2 y - 1$ and $x + y = 2 ∴ A r e a = \frac{5}{4} = \frac{m}{n}$

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Let $C_{1}$ and $C_{2}$ be two curves which satisfy the differential equation $2 {(\frac{d y}{d x})}^{2}$ + $x (\frac{d y}{d x}) = y$ and passes through (1, 1). If the area enclosed by the curves $C_{1}$ , $C_{2}$ and the axes is $\frac{m}{R}$ then m + n = _______________