Question

a) $ y=\sqrt{x}\left(\frac{d y}{d x}\right)+\frac{k}{(d y / d x)} $ b) $ y=x\left(\frac{d y}{d x}\right)+a\left\{1+\left(\frac{d y}{d x}\right)^{2}\right\}^{1 / 2} $ 12 c) $ \left(\frac{d^{2} y}{d x^{2}}\right)^{1 / 3}=\left(y+\frac{d y}{d x}\right)^{1 / 2} $ d) $ \left\{y+x\left(\frac{d y}{d x}\right)^{2}\right\}^{4 / 3}=x\left(\frac{d^{2} y}{d x^{2}}\right) $ Ans.(a)Order 1; Degree 2 (b)Order 1; Degree 2 (c)order 2; degree 2 (d)Order 2, degree 3

          a) \( y=\sqrt{x}\left(\frac{d y}{d x}\right)+\frac{k}{(d y / d x)} \)
b) \( y=x\left(\frac{d y}{d x}\right)+a\left\{1+\left(\frac{d y}{d x}\right)^{2}\right\}^{1 / 2} \)
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c) \( \left(\frac{d^{2} y}{d x^{2}}\right)^{1 / 3}=\left(y+\frac{d y}{d x}\right)^{1 / 2} \)
d) \( \left\{y+x\left(\frac{d y}{d x}\right)^{2}\right\}^{4 / 3}=x\left(\frac{d^{2} y}{d x^{2}}\right) \)
Ans.(a)Order 1; Degree 2 (b)Order 1; Degree 2 (c)order 2; degree 2 (d)Order 2, degree 3

$a) y=√(x)((d y)/(d x))+(k)/((d y / d x)) b) y=x((d y)/(d x))+a{1+((d y)/(d x))^2}^1 / 2 12 c) ((d^2 y)/(d x^2))^1 / 3=(y+(d y)/(d x))^1 / 2 d) {y+x((d y)/(d x))^2}^4 / 3=x((d^2 y)/(d x^2)) Ans.(a)Order 1; Degree 2 (b)Order 1; Degree 2 (c)order 2; degree 2 (d)Order 2, degree 3$

Added by Trevor V.

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