1
TS EAMCET 2023 (Online) 13th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $\frac{d y}{d x}=\sin (x-y)+\cos (x-y)$ is

A

$\log \left|\frac{\tan \frac{(x-y)}{2}+1}{\tan \frac{(x-y)}{2}}\right|=x+C$

B

$\log \left|\frac{\tan \frac{(x-y)}{2}-1}{\tan \frac{(x-y)}{2}}\right|=x+C$

C

$\log \left|\frac{\tan (x-y)-1}{\tan (x-y)}\right|=x+C$

D

$\log \left|\frac{\sin (x-y)+\cos (x-y)}{\cos (x-y)}\right|=x+C$

2
TS EAMCET 2023 (Online) 13th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $x^2 d y-\left(x y-y^2\right) d x=0$ is

A

$y^2=3 x^2 \log (C x)$

B

$y^2=\log x+C$

C

$y \log x=x+C y$

D

$y \log x=x^2+C$

3
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The degree and order of the differential equation of the family of parabolas whose axis is the $X$-axis, are respectively

A
2,2
B
2,1
C
$1,2^{\circ}$
D
3,2
4
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x$ is

A
$\sin ^{-1}\left(\frac{y}{x}\right)=\frac{x}{2}+C$
B
$\sin \left(\frac{x}{y}\right)=\frac{x^2}{2}+C$
C
$\sin \left(\frac{y}{x}\right)=\log |x|+C$
D
$\cos \left(\frac{y}{x}\right)=\log |x|+C$

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