Differential Equations Questions

The solution of the differential equation $du=(16+u^2)dx$ is:

The differential form of the equation $y=a{e}^{-2x}+b{e}^{2x}$ is:

The order and degree of the differential equation $\frac{d^{3}y}{d{x}^3}=4\sqrt{{\left(\frac{dy}{dx}\right)}^3+y^2}$ are respectively:

What is the solution of the differential equation $\ln \left(\frac{dy}{dx}\right)-a=0$?

The differential equation representing the family of curves $y=a\sin (\lambda x+\alpha )$ is:

The solution of the differential equation $\frac{dy}{dx}=\frac{y}{x}+\frac{f(y/x)}{f^{\prime }(y/x)}$ is:

The solution of $\frac{dy}{dx}+2y\tan x=\sin x$ is:

The order and degree of the differential equation $[1+(\frac{dy}{dx}{)}^3{]}^{\frac{7}{3}}=7\frac{d^{2}y}{d{x}^2}$ are respectively:

The order and degree of the differential equation:
$$x{\left(\frac{d^{2}y}{d{x}^2}\right)}^{2/3}=y^2{\left(\frac{dy}{dx}\right)}^{3/2}$$

The curve satisfying the differential equation $ydx+(x-y)dy=0$ and passing through the point $(1,1)$ is:

If at a point on the curve $y=f(x)$ the slope of the line tangent to the curve is equal to $2xy$, then the function $f$ is:

The integrating factor of the differential equation $\frac{dy}{dx}(x\log x)+y=2\log x$ is given by:

Solve the differential equation $xdy-2ydx=0$.

For the given ordinary differential equation, $\frac{dx}{dy}+x{\sec }^{2}y=e^{-\tan y}$, the integrating factor will be equal to:

The order and degree of the differential equation ${\left[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)\right]}^{3/4}=\frac{d^{2}y}{d{x}^2}$ are:

Rate of growth of bacteria is proportional to the number of bacteria present at time. If $x$ is the number of bacteria present at any instant $t$, then which one of the following is correct? (Let the proportional constant equal to $2$)

What is the general solution of $(1+e^x)ydy=e^{x}dx$? (where $c$ is a constant of integration)

What is the degree of the following differential equation?
$$x=\sqrt{1+\frac{d^{2}y}{d{x}^2}}$$

What is the degree of the differential equation ${\left(\frac{d^{3}y}{d{x}^3}\right)}^{3/2}+{\left(\frac{d^{2}y}{d{x}^2}\right)}^2=0$?

The solution of the differential equation $\cos (x+y)dy=dx$ is:

Solve $\frac{dy}{dx}=e^{x-y}(e^x-e^y)$

The solution of $\frac{dy}{dx}=\frac{x+y}{x-y}$ is:

The differential form of the equation $(y-a{)}^2=2bx$ is:

The degree of the given equation is $\frac{dy}{dx}-x={\left(y-x\frac{dy}{dx}\right)}^{-6}$

The function $y=e^{-4x}$ is a solution to the differential equation: