Mathematics - Differential Equation Question with Solution | TestHub

$S_1$ - Equation of parabola is $y^2=\pm 4ax$

$2y\frac{dy}{dx}=\pm 4a$

D.E of parabola $\Rightarrow y^2=2yx\frac{dy}{dx}$

$2\frac{dy}{y}=\frac{dx}{x}$

Which is variable seperable

$S_2$ - Equation of line which is fixed distance. P from origin can be equation of tangent to circle $x^2+y^2=p^2$

Line is $y=mx+p\sqrt{1+m^2}\left(m=\frac{dy}{dx}\right)$

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

So, degree is 2

$S_3$ - Equation of conic whose both axis co-incide with co-ordinate axis is $a{x}^2+b{y}^2=1$

As there are two constants, so order of D.E is 2