List of top Mathematics Questions on Differential equations asked in KCET

Integrating factor of the differential equation $(1 - x^2)\frac{dy}{dx} - xy = 1$ is
$\int x f(x) dx + \frac{f(x)}{2} = 0$, then $f(x)$ is equal to
Sum of the squares of the order and degree (if defined) of a differential equation $2y' + (y'')^2 = \sqrt{y'' - 3}$ is
General solution of the differential equation \[ \frac{dy}{dx} + y \tan x = \sec x \quad \text{is:} \]
If 'a' and 'b' are the order and degree respectively of the differentiable equation \[ \frac{d^2 y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + x^4 = 0, \quad \text{then} \, a - b = \, \_ \_ \]
The angle between the pair of lines \(\frac{x+3}{3} = \frac{y-1}{5} = \frac{z+3}{4}\) and \(\frac{x+1}{1} = \frac{y-4}{4} = \frac{z-5}{2}\) is
The co-ordinates of the foot of the perpendicular drawn from the origin to the plane 2x - 3y + 4z = 29 are
The sum of the degree and order of differential equation \(\left(1 + y_1^2\right)^{\frac{2}{3}} = y_2\) is
The solution of the differential equation \(\frac{dy}{dx} = (x+y)^2\) is
If \(\int \frac{dx}{(x+2)(x^2 + 1)} = a \log |1+x^2| + b \tan^{-1} x + \frac{1}{5} \log |x+2| + c\), then
If \(e^y + xy = e\) the ordered pair \(\left(\frac{dy}{dx},  \frac{d^2y}{dx^2}\right)\) at \(x = 0\) is equal to
If the standard deviations of the numbers - 1, 0, 1, K is \(\sqrt5\), where \(k>0\), then k is equal to
Solution of Differential Equation $xdy - ydx = 0$ represents
The number of solutions of \(\frac{dy}{dx}=\frac{y+1}{x-1}\) when y(1) = 2 is
Solution of Differential Equating xdy – ydx = 0 represents
The general solution of the differential equation x2dy - 2xydx = x4cosx dx is
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves c1y = (c2 + c3)ex+c4 is
The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is
The solution for the differential equation ${ \frac{dy}{y} +\frac{ dx}{x} = 0 }$ is
The solution of differential equation $x \frac {dy}{dx}+2y=x^2$ is
A gardener is digging a plot of land. As he gets tired, he works more slowly. After $' t '$ minutes he is digging at a rate of $\frac {2} {\sqrt {t}} $square metres per minute. How long will it take him to dig an area of $40$ square metres ?
If $\frac {Log\,x}{b-c} = \frac {Log\,y}{c-a}=\frac {Log \,z}{a-b}$ then the value of $ x^{b+c} . y^{c+a}.z^{a+b} $ is
The general solution of $1+\operatorname{Sin}^{2} x=3 \operatorname{Sin} x \cdot \operatorname{Cos} x, \operatorname{Tan} x \neq \frac{1}{2}$ is ......
The real value of ‘α’ for which $\frac{1 -isinα}{1+ 2isinα}$ is purely real is
\(\frac{d}{dx}[cos^2(cot^{-1}\sqrt{\frac{2+x}{2-x}})]\) is