1
VITEEE 2025
MCQ (Single Correct Answer)
+4
-1

The differential equation for all family of line which are at a unit distance from the origin is

A

$\left[y-x \frac{d y}{d x}\right]^2=1-\left[\frac{d y}{d x}\right]^2$

B

$\left[y-x \frac{d y}{d x}\right]^2=1+\left[\frac{d y}{d x}\right]^2$

C

$\left[y+x \frac{d y}{d x}\right]^2=1+\left[\frac{d y}{d x}\right]^2$

D

$\left[y+x \frac{d y}{d x}\right]^2=1-\left[\frac{d y}{d x}\right]^2$

2
VITEEE 2024
MCQ (Single Correct Answer)
+4
-1

The differential equation corresponding to the family of curves $y=e^x(a x+b)$ is

A
$\frac{d^2 y}{d x^2}+Z \frac{d y}{d x}-y=0$
B
$\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+y=0$
C
$\frac{d^2 y}{d x^2}+2 \frac{d y}{d x}+y=0$
D
$\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}-y=0$
3
VITEEE 2023
MCQ (Single Correct Answer)
+4
-1

If $$m$$ and $$n$$ are order and degree of the question $$\left(\frac{d^2 y}{d x^2}\right)^4+8 \frac{\left(d^2 y / d x^2\right)^3}{\left(d^4 y / d x^4\right)^5}+\left(\frac{d^4 y}{d x^4}\right)=x^2+4$$, then $$m-n$$ is equal to

A
2
B
6
C
$$-$$4
D
$$-$$2
4
VITEEE 2023
MCQ (Single Correct Answer)
+4
-1

The solution of $$d y / d x=1+x+y+x y$$ is

A
$$x+y=c(1+x y)$$
B
$$\log (1+x)+x+y=c$$
C
$$\log (1+y)=x+\frac{x^2}{2}+C$$
D
None of these

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