10 Question MCQ (including Assertion)

Solution of the differential equation \(\tan y \sec ^2 x d x+\tan x \sec ^2 y d y=0\) is :

The integrating factor of the differential equation

$$ \frac{d y}{d x}(x \log x)+y=2 \log x \text { is } $$

Integrating factor of \(\frac{x d y}{d x}-y=x^4-3 x\) is :

Integrating factor of the differential equation \(\frac{d y}{d x}+y \tan x-\sec x=0\) is:

If \(p\) and \(q\) are respectively the order and degree of the differential equation \(\frac{\mathrm{d}}{\mathrm{d} x}\left(\frac{\mathrm{dy}}{\mathrm{d} x}\right)^3=0\), then \((\mathrm{p}-\mathrm{q})\) is

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

The differential equation \(y \frac{d y}{d x}+x=c\) represents :

The solution of the differential equation \(\frac{d y}{d x}=\frac{1+y^2}{1+x^2}\) is:

The number of solutions of \(\frac{d y}{d x}=\frac{y+1}{x-1}\) when \(y(1)=2\) is: