AP EAPCET 2024 - 18th May Morning Shift | Differential Equations Question 24 | Mathematics

The differential equation representing the family of circles having their centres of Y -axis is $\left(y_1=\frac{d y}{d x}\right.$ and $\left.y_2=\frac{d^2 y}{d x^2}\right)$

$y_2=y\left(y_1^2+1\right)$

$y_2=x y\left(y_1^2+1\right)$

$x_2=y_1\left(y_1^2+1\right)$

$x y_2=y\left(y_1^2+1\right)$

AP EAPCET 2024 - 18th May Morning Shift

MCQ (Single Correct Answer)

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The general solution of the differential equation $\left(\sin y \cos ^2 y-x \sec ^2 y\right) d y=(\tan y) d r$, is

$\tan y=3 x \cos ^3 y+c$

$x(\sec y+\tan y)=\cos ^2 y+c$

$y \sin y=x^2 \cos ^2 y+c$

$3 x \tan y+\cos ^3 y=c$

AP EAPCET 2024 - 18th May Morning Shift

MCQ (Single Correct Answer)

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The general solution of the differential equation $(x-y-1) d y=(x+y+1) d x$ is

$\tan ^{-1}\left(\frac{y+1}{x}\right)-\frac{1}{2} \log \left(x^2+y^2+2 y+1\right)=0$

$(x-y)+\log (x+y)=c$

$y^2-x^2+x y-3 y-x=c$

$(x-y-1)^2(x+y+1)^3=c$

AP EAPCET 2022 - 5th July Morning Shift

MCQ (Single Correct Answer)

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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, $$f(x)=$$

$$2 \sqrt{3}(x+C)$$

$$x+C$$

$$\frac{x+C}{2 \sqrt{3}}$$

$$\frac{\sqrt{3}}{2}(x+C)$$

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