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1
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The equation which represents the system of parabolas whose axis is parallel to $Y$-axis satisfies the differential equation.

A

$\frac{d^3 y}{d x^3}=0$

B

$\frac{d^3 y}{d x^3}+\frac{d^2 y}{d x^2}=x+y$

C

$\frac{d^2 y}{d x^2}+x y=4 a x$

D

$\frac{d y}{d x}+x y=x^2$

2
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\cos x \frac{d y}{d x}=y \sin x-1, x \neq(2 n+1) \frac{\pi}{2}, n \in Z$ is the differential equation corresponding to the curve $y=f(x)$ and $f(0)=1$, then $f(x)$

A

$(1-x) \sec x$

B

$(1-x) \cos x$

C

$x+\cos x$

D

$x+\sec x$

3
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The general solution of the differential equation $2 d x+d y=(6 x y+4 x-3 y) d x$ is

A

$2 \log |2 x-1|=3 y^2+4 y+C$

B

$\log |3 y+2|=3 x^2-3 x+C$

C

$\log |3 y+2|=x^2-x+C$

D

$\log |2 x-1|=3 y^2-4 y+C$

4
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the equation of the curve which passes through the point $(1,1)$ satisfies the differential equation $\frac{d y}{d x}=\frac{2 x-5 y+3}{5 x+2 y-3}$, then the equation of that curve is
A
$x^{2}+5 x y-y^{2}+3 x-3 y-5=0$
B
$x^{2}+5 x y-y^{2}+3 x+3 y-11=0$
C
$x^{2}-5 x y-y^{2}-3 x-3 y+11=0$
D
$x^{2}-5 x y-y^{2}+3 x+3 y-1=0$
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