List of top Mathematics Questions

The solution of the differential equation \(\displaystyle \frac{dy}{dx}=1+y^2\) is
The particular integral of \(\displaystyle \frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=e^{-2x}\) is
The solution of the differential equation \(\displaystyle \frac{dy}{dx}+\frac{y}{x}=x^2\) under the condition that \(y(1)=1\) is
The solution of the differential equation \(\displaystyle \frac{d^3y}{dx^3}+3\frac{d^2y}{dx^2}+2\frac{dy}{dx}=0\) is
The order of the differential equation whose general solution is \(y=a\sin x+b\cos x\), where \(a\) and \(b\) are arbitrary constants, is
The area bounded by the curve \(y=4x^2\), the \(x\)-axis, the line \(x=0\) and the line \(x=1\) is
The differential equation \(\displaystyle \frac{dy}{dx}=-\left(\frac{x+y}{1+x^2}\right)\) is
The degree of the differential equation \(y' + y = \frac{5}{y'}\) is
\(\displaystyle \int_{0}^{\pi/2}\frac{\cos 2x}{\sin x+\cos x}\,dx=\)
The RMS value of \(x^2\) in \([0,1]\) is
The value of \(\displaystyle \int_0^1 x(1-x)^9\,dx\) is
\(\displaystyle \int_{-a}^{a}|x|\,dx=\)
\(\displaystyle \int \frac{dx}{25-x^2}=\)
For what value of \(x\), the function \(2x^3+3x^2-36x+10\) has minimum?
If \(u=e^{xy}\), then the value of \(\displaystyle \frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2}\) at \((1,1)\) is
\(\displaystyle \int \sin^2x\,dx=\)
The value of \(\displaystyle \int (\log\sec x)\tan x\,dx\) is
If \(z=x^2-y^2\), then \(\displaystyle \frac{1}{x}\frac{\partial z}{\partial x}+\frac{1}{y}\frac{\partial z}{\partial y}=\)
If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots\infty}}}\), then \(\displaystyle \frac{dy}{dx}=\)
\(\displaystyle \frac{d}{dx}\left(\tan^{-1}\frac{x}{a}\right)=\)
The derivative of \(x^x\) with respect to \(x\) is
Slope of the normal to the curve \(x^{2/3}+y^{2/3}=2\) at the point \((1,1)\) is
The equation of the tangent to the curve \(y=x^3\) at \((1,1)\) is
The value of \(\displaystyle \lim_{x\to 1}\left(\frac{x^3-1}{x-1}\right)\) is
The eccentricity of the ellipse \(16x^2+7y^2=112\) is