1
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

Find the solution of $$\frac{d y}{d x}=\frac{1}{\cos (x-y)}$$

A
$$-\cot \left(\frac{x+y}{2}\right)+c$$
B
$$\operatorname{cosec}^2\left(\frac{x+y}{2}\right)+c$$
C
$$\tan \left(\frac{x+y}{2}\right)+c$$
D
$$\cot \left(\frac{x-y}{2}\right)+c$$
2
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

The solution of the equation $$\frac{d y}{d x}+x(x+y)=x^3(x+y)^3-1$$ is

A
$$\frac{1}{(x+y)^2}=x^2+1+c e^x$$
B
$$\frac{1}{(x+y)^2}=x^2+1+c e^x$$
C
$$\frac{1}{(x+y)^2}=x^2+1+c e^{x^2}$$
D
$$\frac{1}{x+y}=x+1+c e^{x^2}$$
3
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

If $$p$$ and $$q$$ are order and degree of the question $$\left(\frac{d^2 y}{d x^2}\right)^4+4 \frac{\left(\frac{d^2 y}{d x^2}\right)^2}{\left(\frac{d^3 y}{d x^3}\right)^3}+\frac{d^3 y}{d x^3}=x^2-1$$, then

A
$$p=3, q=3$$
B
$$p=3, r=2$$
C
$$p=4, r=3$$
D
$$p=3, r=4$$
4
VITEEE 2022
MCQ (Single Correct Answer)
+1
-0

The solution of $$\frac{d y}{d x}=1+x+y+x y$$ is

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