Short Quiz

Question 1 of 5

NCERT Exemplar

The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2\) is

A 1 B 2 C 3 D 4

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Question 2 of 5

NCERT Exemplar

Solution of the differential equation \(\frac{d x}{x}+\frac{d y}{y}=0\) is

A \(\frac{1}{x}+\frac{1}{y}=c\) B \(\log x \cdot \log y=c\) C \(x y=c\) D \(x+y=c\)

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Question 3 of 5

NCERT Exemplar

\(\tan ^{-1} x+\tan ^{-1} y=c\) is the general solution of the differential equation:

A \(\frac{d y}{d x}=\frac{1+y^2}{1+x^2}\) B \(\frac{d y}{d x}=\frac{1+x^2}{1+y^2}\) C \(\left(1+x^2\right) d y+\left(1+y^2\right) d x=0\) D \(\left(1+x^2\right) d x+\left(1+y^2\right) d y=0\)

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Question 4 of 5

NCERT Exemplar

The solution of the differential equation \(x \frac{d y}{d x}+2 y=x^2\) is

A \(y=\frac{x^2+c}{4 x^2}\) B \(y=\frac{x^2}{4}+c\) C \(y=\frac{x^4+c}{x^2}\) D \(y=\frac{x^4+c}{4 x^2}\)

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Question 5 of 5

NCERT Exemplar

Family \(y=\mathrm{A} x+\mathrm{A}^3\) of curves is represented by the differential equation of degree :

A 1 B 2 C 3 D 4

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