TS EAMCET 2022 (Online) 19th July Evening Shift | Differential Equations Question 45 | Mathematics

If $m$ and $n$ are respectively the order and the degree of the differential equation representing the family of curves $y^2-5 a x-5 a^{3 / 2}=0(a>0$ is a parameter), then the value of $m-n$ is

-1

-2

TS EAMCET 2022 (Online) 19th July Evening Shift

MCQ (Single Correct Answer)

-0

The general solution of $\left(\left(1+x^2\right) y \sin x-2 x y\right) d x-\log y^{1+x^2} d y=0$ is

$\sin x-\log \left(1+x^2\right)=\log y+c$

$(\log y)^2+2 \cos x+\log \left(1+x^2\right)^2=c$

$\log y=2 \cos x+\log \left(1+x^2\right)+c$

$\frac{\log y}{y}=2 \sin x+\cos x \log \left(1+x^2\right)+c$

TS EAMCET 2022 (Online) 19th July Morning Shift

MCQ (Single Correct Answer)

-0

The equation of any member of the family of all the ellipses whose axes are along the coordinate axes satisfies the differential equation

$x y^{\prime \prime}+x\left(y^{\prime}\right)^2-y y^{\prime}=0$

$x y y^{\prime \prime}+x\left(y^{\prime}\right)^2-y=y^{\prime}$

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

$y^{\prime \prime}+\left(y^{\prime}\right)^2+x^2 y^2=0$

TS EAMCET 2022 (Online) 19th July Morning Shift

MCQ (Single Correct Answer)

-0

The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^{\frac{4}{3}}+x\left(\frac{d y}{d x}\right)^2-y \cos \left(\frac{d y}{d x}\right)=0$ is

Not defined

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