Differential Equations · Mathematics · NDA

Let $y_1(x)$ and $y_2(x)$ be two solutions of the differential equation $\frac{dy}{dx} = x$. If $y_1(0) = 0$ and $y_2(0) = 4$, then what is the number...

The differential equation, representing the curve $y = e^{x}(a\cos{x} + b\sin{x})$ where $a$ and $b$ are arbitrary constants, is

What are the order and degree respectively of the differential equation $$ \left\{2-\left(\frac{d y}{d x}\right)^2\right\}^{0-6}=\frac{d^2 y}{d x^2} ?...

If $\frac{dy}{dx} = 2e^xy^3$, $y(0)= \frac{1}{2}$ then what is $4y^2(2-e^x)$ equal to?

What is the directrix of the parabola ?

What is the length of latus rectum of the parabola?

What are the order and the degree respectively of the differential equation $\rm x^2\left(\frac{d^3 y}{d x^3}\right)^2+\left(\frac{d y}{d x}...

What is the differential equation of all parabolas of the type y2 = 4a (x - b)?...

What is the order of the differential equation ?

What is the degree of the differential equation ? 

A solution of the differential equation $\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0 $ is

Consider the following statements: 1. The degree of the differential equation $\frac{\text{dy}}{\text{dx}} + \cos \left(\frac{\text{dy}}{\text{d...

What is the differential equation of the family of parabolas having a vertex at origin and axis along positive y-axis?

What is the solution of the differential equation (dy − dx) + cos x(dy + dx) = 0 ?

What is the degree of the differential equation? $1+\left(\frac{dy}{dx}\right)^2 =\left(\frac{d^2y}{dx^2}\right)^{\frac{4}{3}}?$...

If $\frac{dy}{dx} = (\ln 5)y $  with y(0) = ln 5, then what is y(1) equal to?

What does the equation $x \frac{dy}{dx}-2y= 0$ represent ?