1
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The general solution of the differential equation $(x-y-1) d y=(x+y+1) d x$ is
A
$\tan ^{-1}\left(\frac{y+1}{x}\right)-\frac{1}{2} \log \left(x^2+y^2+2 y+1\right)=0$
B
$(x-y)+\log (x+y)=c$
C
$y^2-x^2+x y-3 y-x=c$
D
$(x-y-1)^2(x+y+1)^3=c$
2
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $$\frac{d y}{d x}=\cos ^2(3 x+y)$$ is $$\tan ^{-1}\left(\frac{\sqrt{3}}{2} \tan (3 x+y)\right)=f(x)$$. Then, $$f(x)=$$

A
$$2 \sqrt{3}(x+C)$$
B
$$x+C$$
C
$$\frac{x+C}{2 \sqrt{3}}$$
D
$$\frac{\sqrt{3}}{2}(x+C)$$
3
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the general solution of the differential equation $$\cos ^2 x \frac{d y}{d x}+y=\tan x$$ is $$y=\tan x-1+C e^{-\tan x}$$ satisfies $$y\left(\frac{\pi}{4}\right)=1$$, then $$C=$$

A
e
B
1
C
$$-$$1
D
$$\frac{1}{e}$$
4
AP EAPCET 2022 - 5th July Morning Shift
MCQ (Single Correct Answer)
+1
-0

Assertion (A) Order of the differential equations of a family of circles with constant radius is two.

Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.

A
A and R are true, R is the correct explanation to A
B
A is true, R is false
C
A and R are true, R is not the correct explanation to A
D
A is false, R is true
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