A curve passes through the point left(1, frac | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The slope of the curve is given by $\frac{dy}{dx} = \frac{y}{x} + \sec\left(\frac{y}{x}\right)$.This is a homogeneous differential equation. Let $

Vedclass · Accepted Answer

$\sin \left(\frac{y}{x}\right)=\log x+\frac{1}{2}$

Vedclass · Answer

(A) The slope of the curve is given by $\frac{dy}{dx} = \frac{y}{x} + \sec\left(\frac{y}{x}\right)$.This is a homogeneous differential equation. Let $v = \frac{y}{x}$,so $y = vx$ and $\frac{dy}{dx} = v + x\frac{dv}{dx}$.Substituting these into the equation: $v + x\frac{dv}{dx} = v + \sec(v)$.This simplifies to $x\frac{dv}{dx} = \sec(v)$,which can be rewritten as $\cos(v) dv = \frac{1}{x} dx$.Integrating both sides: $\int \cos(v) dv = \int \frac{1}{x} dx$.This gives $\sin(v) = \ln|x| + C$.Substituting $v = \frac{y}{x}$ back,we get $\sin\left(\frac{y}{x}\right) = \ln|x| + C$.The curve passes through $\left(1, \frac{\pi}{6}\right)$,so $\sin\left(\frac{\pi/6}{1}\right) = \ln(1) + C$.Since $\sin(\pi/6) = 1/2$ and $\ln(1) = 0$,we find $C = 1/2$.Thus,the equation of the curve is $\sin\left(\frac{y}{x}\right) = \ln x + \frac{1}{2}$.

$A$ curve passes through the point $\left(1, \frac{\pi}{6}\right)$. Let the slope of the curve at each point $(x, y)$ be $\frac{y}{x}+\sec \left(\frac{y}{x}\right)$,$x>0$. Then the equation of the curve is

Similar Questions

$A$ micelle formed during the cleansing action by soap is

Give the correct order of electrical conductivity of aqueous solution of the following complexes:
$A. [Pt(NH_3)_6]Cl_4$
$B. [Cr(NH_3)_6]Cl_3$
$C. [Co(NH_3)_4Cl_2]Cl$
$D. K_2[PtCl_6]$

The uncertainties in the velocities of two particles $A$ and $B$ are $0.05 \ m \ s^{-1}$ and $0.02 \ m \ s^{-1}$ respectively. The mass of $B$ is five times that of mass $A$. What is the ratio of uncertainties $\left(\frac{\Delta x_A}{\Delta x_B}\right)$ in their positions?

What is heavy water?

$A$ magnetized wire of magnetic moment $M$ and length $L$ is bent into an arc of a circle subtending an angle of $60^{\circ}$ at the center. The new magnetic moment is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module