Homogeneous Differential Equation

Q.

What is a homogeneous differential equation?

Q. $\frac{dy}{dx}=x^2+y^2$ is a homogeneous differential equation.

1. True
2. False

Q. $\frac{dy}{dx}=x^2+y^2$ is a homogeneous differential equation.

1. True
2. False

Q. The solution of the differential equation $x\frac{dy}{dx}=y(logy-logx+1)$ is

1. $y=x{e}^{cx}$
2. $y+x{e}^{cx}=0$
3. $y+e^x=0$
4. $Noneofthese$

Q. The solution of the differential equation $\frac{dy}{dx}=\frac{x+y}{x}$ satisfying the condition $y\left(1\right)=1$ is

1. $y=\ln x+x$
2. $y=x\ln x+x^2$
3. $y=x{e}^{x-1}$
4. $y=x\ln x+x$

Q. $\frac{dy}{dx}=\frac{x^2+y^2}{2xy}$ is a homogeneous Differential equation because

1. $\frac{(x^2+y^2)}{2xy}$ is not a homogenous function.
2. It is not a homogenous differential equation.
3. $\frac{(x^2+y^2)}{2xy}$ is a homogenous function of degree zero.
4. None of the above.

Q. The solution of $(x^2+xy)dy=(x^2+y^2)dx$ is

1. $\log x=\log (x-y)+\frac{y}{x}+c$
2. $\log x=2\log (x-y)+\frac{y}{x}+c$
3. $\log x=\log (x-y)+\frac{x}{y}+c$
4. $\log x=2\log (x-y)+\frac{x}{y}+c$

Q.

What is a homogeneous differential equation?