1
VITEEE 2023
MCQ (Single Correct Answer)
+1
-0

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
2
VITEEE 2023
MCQ (Single Correct Answer)
+1
-0

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
3
VITEEE 2023
MCQ (Single Correct Answer)
+1
-0

If $$x d y / d x=x^2+y-2, y(1)=1$$, then $$y(2)$$ is equal to

A
2
B
4
C
1
D
8
4
VITEEE 2023
MCQ (Single Correct Answer)
+1
-0

The solution of differential equation $$y y^{\prime}=x\left(\frac{y^2}{x^2}+\frac{f\left(y^2 / x^2\right)}{f^{\prime}\left(y^2 / x^2\right)}\right)$$ is

A
$$x^2 f\left(\frac{y^2}{x^2}\right)=c$$
B
$$x^2 f\left(\frac{y^2}{x^2}\right)=c^2 y^2$$
C
$$f\left(\frac{y^2}{x^2}\right)=c x^2$$
D
$$f\left(\frac{y^2}{x^2}\right)=\frac{c y}{x}$$
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