MHT CET 2026 17th April Evening Shift | Differential Equations Question 20 | Mathematics

The tangent to the curve intersects the Y-axis at point P. A line drawn through point P is perpendicular to this tangent and passes through another point $(1, 0)$. The differential equation of the curve is...

$y\dfrac{dy}{dx} - x\left(\dfrac{dy}{dx}\right)^2 = 1$

$x\dfrac{dy}{dx} - y\left(\dfrac{dy}{dx}\right)^2 = 1$

$y\dfrac{dy}{dx} + x = 1$

$x\dfrac{dy}{dx} + y = 1$

MHT CET 2026 17th April Morning Shift

MCQ (Single Correct Answer)

-0

If $y = e^{-mx}$ is a solution of the differential equation $\dfrac{d^2y}{dx^2} + 4\dfrac{dy}{dx} + 3y = 0$, then the values of $m$ are

$1, 3$

$-1, 3$

$-1, -3$

$1, -3$

MHT CET 2026 17th April Morning Shift

MCQ (Single Correct Answer)

-0

For the differential equation $(x^2 + y^2)\,dy = xy\,dx$, it is given that $y(1) = 1$ and $y(x_0) = e$, then the value of $x_0$ is _____

$e$

$\pm\sqrt{3}\,e$

$3e^2$

$e^2$

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