The order and degree of the differential equa | vedclass

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Question

(A) The equation of a tangent line to the parabola $x^2 = 4y$ with slope $m$ is given by $y = mx - am^2$. Here,$a = 1$,so the equation is $y = mx - m^

Vedclass · Accepted Answer

$1, 2$

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(A) The equation of a tangent line to the parabola $x^2 = 4y$ with slope $m$ is given by $y = mx - am^2$. Here,$a = 1$,so the equation is $y = mx - m^2$. To find the differential equation,we differentiate with respect to $x$: $\frac{dy}{dx} = m$. Substituting $m = \frac{dy}{dx}$ into the original equation,we get: $y = x(\frac{dy}{dx}) - (\frac{dy}{dx})^2$. Rearranging the terms,we have $(\frac{dy}{dx})^2 - x(\frac{dy}{dx}) + y = 0$. The highest order derivative present is $\frac{dy}{dx}$,so the order is $1$. The power of the highest order derivative is $2$,so the degree is $2$.

The order and degree of the differential equation of all tangent lines to the parabola $x^2 = 4y$ are respectively:

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