TS EAMCET 2020 (Online) 11th September Evening Shift | Differential Equations Question 62 | Mathematics

If $\alpha$ and $\beta$ are respectively the order and degree of the differential equation for which $a x^2+b y^2=1$ is the general solution, then the eccentricity of the ellipse $\alpha x^2+\beta y^2=1$ is

$\frac{1}{\sqrt{2}}$

$\frac{1}{2}$

$\frac{1}{2 \sqrt{2}}$

$\frac{1}{\sqrt{2}+1}$

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

The solution of the differential equation $x d y-y d x=\sqrt{x^2+y^2} d x$, given that $y=1$ when $x=\sqrt{3}$, is

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

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

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

TS EAMCET 2020 (Online) 11th September Evening Shift

MCQ (Single Correct Answer)

-0

If the solution $y(x)$ of the differential equation $\sin x \frac{d y}{d x}+y \cos x=e^{2 x}, x \in(0, \pi)$ satisfies $y\left(\frac{\pi}{2}\right)=0$, then $y\left(\frac{\pi}{6}\right)=$

$e^{\pi / 3}+e^\pi$

$e^{\pi / 3}-e^\pi$

$e^\pi-e^{\pi / 3}$

$\frac{1}{2}\left(e^{\pi / 3}-e^\pi\right)$

TS EAMCET 2020 (Online) 11th September Morning Shift

MCQ (Single Correct Answer)

-0

The differential equation for which $l x^2+m y^2=x+y$ is the general solution is

$\left|\begin{array}{ccc}x^2 & y^2 & x+y \\ 2 x & 2 y^{\prime} y & y^{\prime}+1 \\ 2 & 2 y y^{\prime \prime} & y^{\prime \prime}\end{array}\right|=0$

$\left|\begin{array}{ccc}x^2 & y^2 & x+y \\ 2 x & 2 y y^{\prime} & 1+y^{\prime} \\ 2 & 2\left(y^{\prime 2}+y y^{\prime \prime}\right) & y^{\prime \prime}\end{array}\right|=0$

$\left|\begin{array}{ccc}x^2 & y^2 & x+y \\ 2 x & 2 y y^{\prime} & y+1 \\ 2 & 2\left(y^{\prime 2}+y^{\prime} y^{\prime \prime}\right) & y^{\prime \prime}\end{array}\right|=0$

$\left|\begin{array}{ccc}x^2 & y^2 & x+y \\ 2 x & 2 y & 1+y^{\prime} \\ 2 & 2 y y^{\prime} y^{\prime \prime} & y^{\prime \prime}\end{array}\right|=0$

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