Differential Equations

Let $y=y_{1}\left(x\right)$and$y=y_{2}\left(x\right)$bethesolution curves thedifferential equation$\frac{dy}{dx}=y+7$ with initialconditions$y_{1}\left(0\right)=0$ and$y_{2}\left(0\right)=1$ respectively. Then the…

The degree and order respectively of the differential equation $\frac{d y}{d x}=\frac{1}{x+y+1}$ are

Paragraph: Let $y d x+\left(x-y^3\right) d y=0$ be a differential equation. Question: What are the order and degree respectively of the differential equation?

What is the order of the differential equation whose solution is $\mathrm{y}=\mathrm{a} \cos \mathrm{x}+\mathrm{b} \sin \mathrm{x}+\mathrm{ce}^{-\mathrm{x}}+\mathrm{d}$, where $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and d…

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

What is the solution of the differential equation $\frac{y d x-x d y}{y^2}=0 ?$ where $c$ is an arbitrary constant?

What is the general solution of the differential equation $\frac{d y}{d x}+\frac{x}{y}=0$ ?

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

The order and degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^3=\rho^2\left[\frac{d^2 y}{d x^2}\right]^2 \quad$ are respectively

What is the solution of the differential equation $x d y-y d x=0 ?$

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

What are the order and degree respectively of the differential equation $\left\{2-\left(\frac{d y}{d x}\right)^2\right\}^{0.6}=\frac{d^2 y}{d x^2}$ ?