List of top Mathematics Questions on Differential equations asked in MHT CET

The general solution of the differential equation \(\frac{dy}{dx}+\frac{y}{x} = x^2+5\) is ....

If \(y = f(x)\) is a monotonically increasing function such that \((\frac{dy}{dx})^2 = 6-\frac{dy}{dx}\) and \(y(0) = 5\), then \(y(3) = \cdots\)

If \(tanx\) is an integrating factor of the differential equation \(\frac{dy}{dx}+Py = Q\), then \(P\) can be

The solution of the differential equation \(\frac{dy}{dx} = cos(x+y)\) is...

The differential equation of all lines where the length of the normal from the origin is p and the inclination of the normal is \(α\) is... (where p and \(α\) are arbitrary constants)

If the solution of the differential equation \((1+x^3)\frac{dy}{dx}+6x^2y = 1+x^2\) is \(y = \frac{1}{(1+x^3)^s}[x+\frac{x^p}{p}+\frac{x^q}{q}+\frac{x^r}{r}+c]\), then the LCM of \(p,q,r\) and \(s\) is...

The solution of the differential equation \(\frac{dy}{dx} = \frac{x-y}{x+y}\), when \(x = 0\) and \(y = 0\) represents ....

The differential equation of the family of all parabolas whose axis is the \(y\)-axis is \(\ldots\)

The integrating factor of the differential equation \(x\frac{dy}{dx}+2y = x^2logx\) is

A spherical raindrop evaporates at a rate proportional to its surface area. The differential equation involving the rate of change of its radius \(r\) with time '\(t\)' is \(\ldots\) (where \(k\) is a positive constant)

The rate of disintegration of a radioactive element at any time is proportional to its mass at that time, where \(k\) \((k > 0)\) is the constant of proportionality. The time during which an original mass of 1.5 gm will disintegrate to a mass of 0.5 gm is \(\ldots\)

The equation of the curve whose slope is \(\frac{y-1}{x^2+x}\) and which passes through the point \((1,0)\) is

A body cools from \(100^{\circ}\text{C}\) to \(60^{\circ}\text{C}\) in 20 minutes, the temperature of the surroundings being \(20^{\circ}\text{C}\). The total time taken (in minutes) for the body to cool down to \(40^{\circ}\text{C}\) is ...

The general solution of the differential equation \(xsinx\frac{dy}{dx}+(xcosx+sinx)y = sinx\) is

The general solution of the differential equation \(secy+(x-e^{siny})\frac{dy}{dx} = 0\) is...

Let \(f(x) = x-[x]\) for every real number \(x\), where \([x]\) is integral part of \(x\). then \(\int _{-1}^1f(x)\,dx\) is

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...

If water at \(100^{\circ}\text{C}\) cools in 10 minutes to \(80^{\circ}\text{C}\) and to \(65^{\circ}\text{C}\) in the next 10 minutes, then the room temperature will be ...

The solution of the differential equation \((x+2y^3)\frac{dy}{dx}-y = 0\) is

The rate of reduction is proportional to the square root of a persons existing assets at that moment. If his assets at the beginning are 10000 and they dwindle down to 5625 in 2 years, then the person will be bankrupt in

The integrating factor of the differential equation \((1+t^2)+(x-e^{tan^{-1}t})\frac{dt}{dx} = 0\) is

The solution of \(\frac{\text{d}y}{\text{d}x} = sin(x+y)+cos(x+y)\) is

The solution of the differential equation \(e^{-x}(y+1)\text{d}y+(cos^2x-sin2x)y\,\text{d}x = 0\), given that \(y = 1\) when \(x = 0\) is

The solution of the differential equation \(\frac{dy}{dx} = e^{x-y}+x^2e^{-y}\) is...

If the differential equation \(\begin{array}{cc}f(x) & f^'(x) \\ f^'(x) & f^{''}(x)\end{array} = 0\) for all \(x\) and \(f(0) = 1,f^'(0) = 2\), then...