Differential Equations · Mathematics · AP EAPCET
MCQ (Single Correct Answer)
If $y=A t^2+\frac{B}{t}$ ( $A, B$ are parameters) is general solution of the differential equation $f(t) y^{\prime \prime}(t)+g(t) y^{\prime}(t)+h(t) y=0$ then $2 f(t)+t^2 h(t)=$
The general solution of the differential equation $(2 x-y)^2 d y-2(2 x-y)^2 d x-2 d x=0$ is
The general solutions of the differential equation $x \log x d y=(x \log x-y) d x$ is
The general solution of the differential equation $\left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x$ is
The general solution of the differential equation $\cos (x+y) d y=d x$ is
If $A x^3+B x y=4$ ( $A$ and $B$ are arbitrary constants) is the general solution of the differential equation $F(x) \frac{d^2 y}{d x^2}+G(x) \frac{d y}{d x}-2 y=0$, then $F(l)+G(l)=$
If $a$ and $b$ are arbitrary constants, then the differential equation corresponding to the family of curves $y=\tan (a x+b)$ is
The general solution of the differential equation $x y(y+2) d y+\left(y^3-1\right) d x=0$ is
The general solution of the differential equation $\left(1+\sin ^2 x\right) \frac{d y}{d x}+y \sin 2 x=\cos x+\sin ^2 x \cos x$ is
The solution of the differential equation $x^2(y+1) \frac{d y}{d x}+y^2(x+1)^2=0$, when $y(1)=2$, is
The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x+y-3}{2 y-x+3}$
If $x \log x \frac{d y}{d x}+y=\log x^2$ and $y(e)=0$, then $y\left(e^2\right)=$
If the order and degree of the differential equation $x \frac{d^2 y}{d x^2}=\left(1+\left(\frac{d^2 y}{d x^2}\right)^2\right)^{-1 / 2}$ are $k$ and $l$ respectively, then $k, l$ are the roots of
The equation of the curve passing through the point $(0, \pi)$ and satisfying the differential equation $y d x=\left(x+y^3 \cos y\right) d y$ is
The general solution of the differential equation $(x-(x+y) \log (x+y)) d x+x d y=0$ is
The general solution of the differential equation $\sec (x-y+1) d y=d x$ is
The differential equation of the family of circles passing through the origin and having centre on $X$-axis is
The general solution of the differential equation $\frac{d y}{d x}=\frac{x+y}{x-y}$ is
The general solution of the differential equation $\frac{d y}{d x}+\frac{\sec x}{\cos x+\sin x} y=\frac{\cos x}{1+\tan x}$ is
The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x^2-x y-y^2}{x^2-y^2}$ is
If the degree of the differential equation corresponding to the family of curves $y=a x+\frac{1}{a}$ (where $a \neq 0$ is an arbitary constant) is $r$ and it's order is $m$. Then, the solution of $\frac{d y}{d x}=\frac{y}{2 x}, y(\mathrm{l})=\sqrt{r+m}$ is
The general solution of the differential equation $y+\cos x\left(\frac{d y}{d x}\right)-\cos ^2 x=0$ is
The general solution of the differential equation $\frac{d y}{d x}+x y=4 x-2 y+8$ is
The general solution of the differential equation $\left(x+2 y^3\right) \frac{d y}{d x}-y=0, y>0$ is
The general solution of the differential equation $\frac{d y}{d x}+\frac{x+y+1}{x-3 y+5}=0$ is
The differential equation corresponding to the family of parabolas whose axis is along $x=1$ is
The general solution of the equation $\frac{d y}{d x}+\frac{1}{x} y=\frac{1}{x} e^x$
The general solution of the differential equation
$$ \left(x \sin \frac{y}{x}\right) d y=\left(y \sin \frac{y}{x}-x\right) d x $$
The general solution of the differential equation $\left(x y+y^2\right) d x-\left(x^2-2 x y\right) d y=0$ is
The sum of the order and degree of differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{1 / 2}=\left(1+\frac{d y}{d x}\right)^{4 / 3}$
$\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x} \Rightarrow \sin \frac{y}{x}=$
$$ \begin{aligned} &\text { The general solution of the differential equation }\\ &(x+y) y d x+(y-x) x d y=0 \text { is } \end{aligned} $$
The general solution of the differential equation $$\frac{d y}{d x}=\cos ^2(3 x+y)$$ is $$\tan ^{-1}\left(\frac{\sqrt{3}}{2} \tan (3 x+y)\right)=f(x)$$. Then, $$f(x)=$$
If the general solution of the differential equation $$\cos ^2 x \frac{d y}{d x}+y=\tan x$$ is $$y=\tan x-1+C e^{-\tan x}$$ satisfies $$y\left(\frac{\pi}{4}\right)=1$$, then $$C=$$
Assertion (A) Order of the differential equations of a family of circles with constant radius is two.
Reason (R) An algebraic equation having two arbitrary constants is general solution of a second order differential equation.
If $$l$$ and $$m$$ are order and degree of a differential equation of all the straight lines at constant distance of $$P$$ units from the origin, then $$l m^2+l^2 m=$$
If $$2 x-y+C \log (|x-2 y-4|)=k$$ is the general solution of $$\frac{d y}{d x}=\frac{2 x-4 y-5}{x-2 y+2}$$, then $$C=$$
By eliminating the arbitrary constants from $$y=(a+b) \sin (x+c)-d e^{x+e+f}$$, then differential equation has order of
If the solution of $$\frac{d y}{d x}-y \log _e 0.5=0, y(0)=1$$, and $$y(x) \rightarrow k$$, as $$x \rightarrow \infty$$, then $$k=$$
$$y=A e^x+B e^{-2 x}$$ satisfies which of the following differential equations?
If $$y=\sin (\sin x)$$ and $$y^{\prime \prime}+f(x) \cdot y^{\prime}+g(x) \cdot y=0$$, then $$f(x) \cdot g(x)$$ is equal to
The equation of the curve passing through the point $$\left(0, \frac{\pi}{4}\right)$$ and satisfying the differential equation $$\left(e^x \tan y\right) d x\left.+\left(1+e^x\right) \sec ^2 y\right) d y=0$$ is given by
The solution of the differential equation $$2x\left(\frac{dy}{dx}\right)-y=4$$ represents a family of
The solution of the differential equation $$\frac{d^2 y}{d x^2}+y=0$$ is