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The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x+2}{3-y}, (y \neq 3), y(0) = 0$

represents

General solution of the differential equation $x(xdy - ydx) = y\,dx$ is :(where c is an arbitrary constant)

If the order and degree of the differential equation $y + \dfrac{dy}{dx} = \int y\,dx$ are m and n respectively, then (m - n) is equal to

General solution of the differential equation $(1+x^2)dy + 2xy\,dx = \cot x\,dx$ is:

(where $C$ is an arbitrary constant)

If $\dfrac{dy}{dx} = e^{x-y} + x^2e^{-y}$, then the solution of the differential equation will be:-

The order and degree of the differential equation $\dfrac{d^3y}{dx^3} + \left(\dfrac{d^2y}{dx^2}\right)^2 + e^{\frac{dy}{dx}} = 2$ is

General solution of the differential equation $(e^x + e^{-x})dy = (3e^{2x} + 3e^{4x})dx$ is:

[Where C is an arbitrary constant]

The product of order and degree of the differential equation

$x\dfrac{d^3y}{dx^3} = \left(1 + \left(\dfrac{dy}{dx}\right)^2\right)^4$ is

General solution of the differential equation $\dfrac{3ydx - 2xdy}{y} = 0$ is :

[where $c$ is an arbitrary constant]

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Which of the following is a homogeneous differential equation ?

If m and n are the order and the degree of the differential equation :

$x\dfrac{d^2y}{dx^2} = \left[1+\left(\dfrac{dy}{dx}\right)^2\right]^{1/3}$ then which one of the following is TRUE?

For a given differential equation $e^{dy/dx} = x + 1; x \in (-1,\infty)$, then which of the following statements are TRUE?

(A) Its general solution is $y = x\log_e(x+1) - x + \log_e(x+1) + C$; C is an arbitrary constant.

(B) Its particular solution is $y = (x+1)\log_e(x+1) - x + 5; y(0) = 5$

(C) Its general solution is $y = (x-1)\log(x+1) - x + C$; C is an arbitrary constant

(D) Its particular solution is $y = (x-1)\log(x+1) - x + 5; y(0) = 5$

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The general solution of the differential equation $\frac{dy}{dx} = \frac{3e^{2x}+3e^{4x}}{e^x+e^{-x}}$ is

The product of the order and degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^2 - 3\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^4 = y^4$ is

Particular solution of the differential equation $dy = e^{2x+y}dx$, $y(0) = 0$ is:

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Let y(x) be the solution curve of the differential equation $x(1+y^2)dx - y(1+x^2)dy = 0$ and it passes through the point (0, 1), then

The differential equation whose order and degree are 3 and 2 respectively is

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

The particular solution of the differential equation $dy=e^{2x+y}dx, y(0)=0$ is

General solution of the differential equation $\frac{dy}{dx}=e^{\frac{x^2}{2}}+xy$ is: (where C is an arbitrary constant)

Integrating factor of the differential equation $x(x-1)\frac{dy}{dx}-(x-2)y=x^3(2x-1), x>1$ is:

The particular solution of the differential equation $\log\left(\frac{dy}{dx}\right)=3x+4y$, given that $y=0$, when $x=0$ is:

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Let $y = f(x)$ be the solution curve of the differential equation $\dfrac{dy}{dx} + 2y^2 = 0$ if $f(1) = 1$, then $f(2)$ is equal to

Which of the following differential equations has $y = x$ as one of its particular solution?

The general solution of the differential equation $(y-x)dy + (x+y)dx = 0$ is: (where C is arbitrary constant)

consider the differential equation $\dfrac{dx}{dy} + Px = Q$, where $P$ and $Q$ are function of $y$. Then

A. Its integrating factor (I.F.) is $e^{\int Pdy}$

B. Its integrating factor (I.F.) is $e^{\int Pdx}$

C. Its solution is given by $x(I.F.) = \int Q(I.F.)dy + C$

D. Its solution is given by $y(I.F.) = \int Q(I.F.)dx + C$

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Match the differential equation (List-I) with its order and degree (List-II)

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