List of top Mathematics Questions on types of differential equations

The differential equation is \[ \frac{dy}{dx}+y\tan x=\sec x \] and \(y(0)=1\). Then the value of \(y\left(\frac{\pi}{4}\right)\) is
The general solution of the differential equation \[ \frac{dy}{dx}=e^{x-y}+x^2e^{-y} \] is
If \(a\) and \(b\) are arbitrary constants, then the differential equation representing the family of curves \[ y=a\sin(x+b) \] is
The order of the differential equation of all circles passing through the origin and having their centres on the \(x\)-axis is
Degree of the differential equation \[ y=x\frac{dy}{dx}+a\sqrt{1+\left(\frac{dy}{dx}\right)^2} \] is
The solution of the differential equation \[ x\frac{dy}{dx}+y=0 \] passing through the point \((1,1)\) is \(y=\)
Let $y = f(x)$ be the real valued function defined on the interval $(0, \infty)$, satisfying $f(1) = 0$ and the differential equation \[ x \frac{dy}{dx} = y - x^3. \] Then which of the following statements is (are) TRUE?
Let \(y : (-\infty, \infty) \to (0, \infty)\) be the solution of the differential equation \[ \frac{dy}{dx} = \frac{e^{5x}y^3 + y^3}{e^x + e^x y^4} \] satisfying \[ y(0) = \frac{1}{\sqrt{2}}. \] Then the value of \[ y(\log_e 2) \] is:
The population \( p(t) \) of a certain mouse species follows \[ \frac{dp}{dt} = 0.5p - 450. \] If \( p(0)=850 \), then the time at which population becomes zero is:}
If \[ x = \int_0^y \frac{1}{\sqrt{1+9t^2}} \, dt \quad \text{and} \quad \frac{d^2 y}{dx^2} = ay, \] then \( a \) is equal to:
The particular integral of \(\displaystyle \frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=e^{-2x}\) is
The solution of the differential equation \(\displaystyle \frac{d^3y}{dx^3}+3\frac{d^2y}{dx^2}+2\frac{dy}{dx}=0\) is
The solution of the differential equation \(\displaystyle \frac{dy}{dx}+\frac{y}{x}=x^2\) under the condition that \(y(1)=1\) is
The differential equation \(\displaystyle \frac{dy}{dx}=-\left(\frac{x+y}{1+x^2}\right)\) is
The degree of the differential equation \(y' + y = \frac{5}{y'}\) is
The solution of the differential equation \(\displaystyle \frac{dy}{dx}=1+y^2\) is
The order of the differential equation whose general solution is \(y=a\sin x+b\cos x\), where \(a\) and \(b\) are arbitrary constants, is
The solution of the differential equation \(\displaystyle \frac{dy}{dx}=1+y^2\) is
The solution of the differential equation \(\displaystyle \frac{dy}{dx}+\frac{y}{x}=x^2\) under the condition that \(y(1)=1\) is
The particular integral of \(\displaystyle \frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=e^{-2x}\) is
The solution of the differential equation \(\displaystyle \frac{d^3y}{dx^3}+3\frac{d^2y}{dx^2}+2\frac{dy}{dx}=0\) is
The differential equation \(\displaystyle \frac{dy}{dx}=-\left(\frac{x+y}{1+x^2}\right)\) is
The degree of the differential equation \(y' + y = \frac{5}{y'}\) is
The order of the differential equation whose general solution is \(y=a\sin x+b\cos x\), where \(a\) and \(b\) are arbitrary constants, is
Which of the following transformations reduce the differential equation
\[ \frac{dz}{dx} + \frac{1}{x} \log z = \frac{1}{x^2} (\log z)^2 \] into the form \[ \frac{du}{dx} + P(x)\,u = Q(x) \] ?