Fill in the blanks of the following ( \( \mathrm{i} \) to \( x i \) )
(i) The degree of the differential equation \( \frac{d^{2} y}{d x^{2}}+e^{\frac{d y}{d x}}=0 \) is
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(ii) The degree of the differential equation \( \sqrt{1+\left(\frac{d y}{d x}\right)^{2}}=x \) is
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(iii) The number of arbitrary constants in the general solution of a differential equation of order three is
(iv) \( \frac{d y}{d x}+\frac{y}{x \log x}=\frac{1}{x} \) is an equation of the type
(v) General solution of the differential equation of the type \( \frac{d x}{d y}+\mathrm{P}_{1} x=\mathrm{Q}_{1} \) is given by
(vi) The solution of the differential equation \( \frac{x d y}{d x}+2 y=x^{2} \) is
(vii) The solution of \( \left(1+x^{2}\right) \frac{d y}{d x}+2 x y-4 x^{2}=0 \) is
(viii) The solution of the differential equation \( y d x+(x+x y) d y=0 \) is
(ix) General solution of \( \frac{d y}{d x}+y=\sin x \) is
(x) The solution of differential equation coty \( d x=x d y \) is
(xi) The integrating factor of \( \frac{d y}{d x}+y=\frac{1+y}{x} \) is
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