Differential Equations Questions

The differential equation whose solution is $A{x}^2+B{y}^2=1$, where $A$ and $B$ are arbitrary constants, is of:

The differential equation of all circles passing through the origin and having their centres on the $x$ -axis is:

The differential equation representing the family of curves $y^2=2c(x+\sqrt{c})$, where $c>0$ is a parameter, is of order and degree respectively:

If $x\frac{dy}{dx}=y(\log y-\log x+1)$, then the solution of the equation is:

The degree and order of the differential equation of the family of all parabolas whose axis is the $x$ -axis, are respectively:

The solution of the differential equation $(1+y^2)+(x-e^{{\tan }^{-1}y})\frac{dy}{dx}=0$, is:

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

The differential equation of the family of circles with fixed radius $5$ units and centre on the line $y=2$ is:

The differential equation which represents the family of curves $y=c_1{e}^{c_{2}x}$, where $c_1$ and $c_2$ are arbitrary constants is:

Solution of the differential equation $\cos xdy=y(\sin x-y)dx$, $0<x<\frac{\pi }{2}$ is:

If $\frac{dy}{dx}=y+3>0$ and $y(0)=2$, then $y(\ln 2)$ is equal to:

Let $I$ be the purchase value of an equipment and $V(t)$ be the value after it has been used for $t$ years. The value $V(t)$ depreciates at a rate given by differential equation $\frac{dV(t)}{dt}=-k(T-t)$, where $k>0$ is a constant and $T$ is the total life in years of the equipment. Then the scrap value $V(T)$ of the equipment is:

The population $p(t)$ at time $t$ of a certain mouse species satisfies the differential equation $\frac{dp(t)}{dt}=0.5p(t)-450$. If $p(0)=850$, then the time at which the population becomes zero is:

The differential equation for the family of curves $x^2+y^2-2ay=0,$ where $a$ is an arbitrary constant is

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