List of top Mathematics Questions on Differential Equations

Find the particular solution of the differential equation \( \frac{dy}{dx} - 3y \cot x = \sin 2x \), given that \( y = 2 \) when \( x = \frac{\pi}{2} \).

Assertion (A) : One of the particular solutions of the differential equation \( \frac{dy}{dx} = e^{x+y} \) can be \( e^x + e^{-y} = -2 \).
Reason (R) : \( e^x + e^{-y} = C \) is the general solution of the differential equation \( \frac{dy}{dx} = e^{x+y} \).

Find the general solution of the differential equation: \( y \log_e y \frac{dx}{dy} + x = \frac{y^2}{2} \).

The general solution of $\frac{ydx - xdy}{y^2} = 0$ represents a family of}

Which of the following is an integrating factor for the differential equation $x \cos x \frac{dy}{dx} + (x \sin x + \cos x) y = 1$?

$\frac{dy}{dx} = xy + x + y + 1$ has the solution}

If the solution $y(x)$ of the given differential equation $(e^y+1) \cos x dx + e^y \sin x dy = 0$ passes through the point $(\pi/2, 0)$ then the value of $y(\pi/6)$ is

The equation of the curve passing through the origin and satisfying the differential equation $\frac{dy}{dx} = (x-y)^2;$

The differential equation of the family of concentric circles with Centre at the origin is

If the order and degree of a differential equation $(\frac{d^4y}{dt^4} + \frac{d^2y}{dt^2})^{5/2} = 10 \frac{d^3y}{dt^3}$ are $p$ and $q$, respectively, then $p+q =$

The particular integral of $\left(D^4 - D^3 - 9D^2 - 11D - 4\right)y = e^{-x}$, where $D = \frac{d}{dx}$, is:}

The maximum value of \(x^{4}y^{3}\) such that \(x+y=42\) exists at \(x=\alpha,\; y=\beta\). Then \(\dfrac{\alpha}{\beta}\) in its lowest form is

Evaluate \[ \int_{-1}^{1}\frac{x^{2}\sin x}{x^{4}+1}\,dx. \]

If the solution of \[ \frac{d^2y}{dt^2} = -\frac54y+\frac{dy}{dt}, \] satisfying \[ y(0)=1, \qquad \left(\frac{dy}{dt}\right)_{t=0}=0, \] is \(y(t)\), then \(y(\pi)=\)

The general solution of the differential equation \[ (x+y-1)\,dy=(x-y+1)\,dx \] is

The general solution of the differential equation \[ \frac{dy}{dx}=\frac{2xy-3y^2}{2x^2+3xy} \] is

If \(a\) and \(b\) are arbitrary constants, then the differential equation corresponding to the family of curves \[ ax^2+2hxy=1 \] is

Solve $(1+y^2)+(x-e^{-\tan^{-1}y})\frac{dy}{dx}=0$

Solve $\cos(x+y)dy=dx$

Eliminate constants from $y=A(x+B)^2$

Among the following differential equations, the equation having order 2 and degree 3 is:

The general solution of the differential equation \( \frac{dy}{dx} + y \tan x = - \tan x \log(\cos x) \) (\(0 < x < \pi/2\)) is:

Consider the differential equations \(\frac{dy}{dx}(x+y+1)=1\) and \(\frac{dx}{dy}=3y+2x^2\).
Which of the following is correct regarding these two differential equations?

The substitution required to reduce the differential equation \( \frac{dy}{dx}+\sin y \cos y \sin x = \sin 2x \cos^{2}y \) to a linear differential equation in z is

The differential equation among the following, whose general solution is \( y=A e^{5x}+B e^{-4x} \) is