10 Question MCQ (including Assertion)

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

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

\(\frac{d y}{d x}=F(x, y)\) will be a homogeneous differential equation for which of the following functions?
(i) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=3 \mathrm{x}+2 \mathrm{y}\)
(ii) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=\sin \frac{\mathrm{y}}{\mathrm{x}}+\log \mathrm{y}-\log \mathrm{x}\)
(iii) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=\mathrm{e}^{\mathrm{y} / \mathrm{x}}+1\)
(iv) \(\mathrm{F}(\mathrm{x}, \mathrm{y})=\sqrt{\mathrm{x}^{2}+\mathrm{y}^{2}}-\mathrm{y}\)

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

The general solution of \(\frac{d y}{d x}=2 x e^{x^2-y}\) is :

The degree of the differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3+6 y^5=0\) is :

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