TG EAPCET 2025 (Online) 3rd May Morning Shift | Differential Equations Question 7 | Mathematics

The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line $y=2 x$ and eccentricity is $\sqrt{3}$ is

$(2 x-y) y_2+y_1^2-2 y_1=y_1^3+2$

$(y-2 x) y_2+y_1^2+2 y_1=y_1^3+2$

$(y-2 x) y_2-y_1^2+2 y_1=y_1^3-2$

$(y+2 x) y_2+y_1^2+2 y_1=y_1^3-2$

TG EAPCET 2025 (Online) 3rd May Morning Shift

MCQ (Single Correct Answer)

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The general solution of the differential equation $\left(x^3-y^3\right) d x=\left(x^2 y-x y^2\right) d y$ is

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

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

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

$x+y+\log |x+y| c=0$

TG EAPCET 2025 (Online) 2nd May Evening Shift

MCQ (Single Correct Answer)

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The substitution required to reduce the differential equation $t^2 d x+\left(x^2-t x+t^2\right) d t=0$ to a differential equation which can be solved by variables separable method is

$t=V_x$

$a x+b t=Z$

$V=t x^2$

$x=t V^2$

TG EAPCET 2025 (Online) 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

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

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

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

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

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

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