List of top Mathematics Questions on Differential equations

If \[ \frac{dy}{dx} - \frac{2x}{x^2+b}y = -2x(x^2+b), \] with \[ y(0)=12,\qquad y(1)=10, \] then the sum of all possible values of \(b\) is:

If \[ \frac{dy}{dx} = (x^3-x) -(1-3x^2)\tan x +(x^3-x)\tan^2x \] and \[ y(1)=0, \] then \[ \frac{64}{\pi}y\!\left(\frac{\pi}{4}\right) = ? \]

Differential equation for family \(y=ae^{2x}+bx^2\) is

The integrating factor of the linear differential equation in \(x\) given by \[ \frac{dy}{dx}=\frac{1}{3x+y+2} \] is

The solution of the differential equation \[ \frac{dy}{dx} = \frac{3^{x+y}-2\cdot3^x} {3^{x+y}-2\cdot3^y} \] when \[ y(1)=2 \] is:

The solution of the differential equation $x \frac{dy}{dx} + 2y = x^2$ is:

The integrating factor of the differential equation $(1 + x^2) \frac{dy}{dx} + 2xy = \cos x$ is:

The general solution of the differential equation $\frac{dy}{dx} + y \cot x = 2 \cos x$ is:

The general solution of the differential equation \[ (2xy+y^2)\,dy=(x^2-y^2)\,dx \] is:

If the general solution of the differential equation \[ \frac{dy}{dx} + \frac{2x+2y-1}{x+y-5} = 0 \] is \[ ax+by-9\log(x+y+p)=c, \] and \(b,a,p\) are in G.P., then the common ratio of this G.P. is

If \(y=f(x)\) satisfies \[ \tan x \frac{dy}{dx}+(1+\tan^2 x)y=\tan x(1+\tan^2 x)^2 \] and passes through \(\left(\frac{\pi}{4},\frac{3}{4}\right)\), find \(f\left(\frac{\pi}{3}\right)\)

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

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

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

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 \(\ldots\)

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

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

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 ...