Find {d² y}{d x²}, if {x+y}+{y-x}=c

Correct Answer is : 2c2{2}{c²}c22

Correct Answer is : 2c2{2}{c²}c22

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Army Group X Solved Paper

Question : 41 of 50

Marks: +1, -0

Find

\frac{d^{2} y}{d x^{2}},

\sqrt{x+y}+\sqrt{y-x}=c

Solution:

\sqrt{x+y}+\sqrt{y-x}=c

\sqrt{x+y}=c-\sqrt{y-x}

On squaring both sides, we get

x+y=c^{2}+y-x-2c\sqrt{y-x}

\Rightarrow 2x-c^{2}=-2c\sqrt{y-x}

Again, on squaring both sides, we get

4x^{2}+c^{4}-4c^{2}x=4c^{2}(y-x)

\Rightarrow 4x^{2}+c^{4}-4c^{2}x=4c^{2}y-4c^{2}x

\Rightarrow 4c^{2}y=4x^{2}+c^{4}

Differentiation w.r.t.

x

4c^{2} \cdot \frac{dy}{dx}=8x \Rightarrow \frac{dy}{dx}=\frac{2x}{c^{2}}

Differentiation again w.r.t.

x

\frac{d^{2} y}{d x^{2}}=\frac{2}{c^{2}}

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