Question:
The solution of
$\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is
The solution of
$\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is
Updated On: Apr 26, 2024
- x = c sin (y/x)
- x = c sin (xy)
- y = c sin (y/x)
- xy = c sin (x/y)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Given, $\frac{d y}{d x}=\frac{y}{x}+\tan \frac{y}{x}$
Put $y=v x \Rightarrow \frac{d y}{d x}=x \frac{d v}{d x}+v$
$\therefore x \frac{d v}{d x}+v=v+\tan v$
$\Rightarrow \cot v\, d v=\frac{1}{x} d x$
On integrating both sides, we get
$\Rightarrow \log c+\log \sin v =\log x \\ c \sin v =x $
$\Rightarrow x=c \sin \left(\frac{y}{x}\right)$
Was this answer helpful?
3
0
Top Questions on integral
- The value of the integral \( \int_0^1 x^2 \, dx \) is:
- The value of the definite integral \( \int_0^{\pi} \sin^2 x \, dx \) is:
- Let $ f(x) $ be a positive function and $I_1 = \int_{-\frac{1}{2}}^1 2x \, f\left(2x(1-2x)\right) dx$ and $I_2 = \int_{-1}^2 f\left(x(1-x)\right) dx.$ Then the value of $\frac{I_2}{I_1}$ is equal to ____
The integral \(\int e^x \sqrt{e^x} \, dx\) equals:
- The order and degree of the differential equation \( \sqrt{\frac{dy}{dx}} - 4 \frac{dy}{dx} - 7x = 0 \) are respectively
View More Questions
Questions Asked in WBJEE exam
- If 1000! = 3n × m, where m is an integer not divisible by 3, then n =?
- WBJEE - 2024
- Probability
- Chords AB CD of a circle intersect at right angle at the point P. If the lengths of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is:
- If the relation between the direction ratios of two lines in \(\mathbb{R}^3\) are given by \(l + m + n = 0\), \(2lm + 2mn - ln = 0\), then the angle between the lines is:
- WBJEE - 2024
- Vectors
- If \(a, b, c\) are distinct odd natural numbers, then the number of rational roots of the equation \(ax^2 + bx + c = 0\) is:
- WBJEE - 2024
- Quadratic Equation
- What force \(F\) is required to start moving this 10 kg block shown in the figure if it acts at an angle of \(60^\circ\) as shown? (\(\mu_s = 0.6\)).
- WBJEE - 2024
- laws of motion
View More Questions
Concepts Used:
Integral
The representation of the area of a region under a curve is called to be as integral. The actual value of an integral can be acquired (approximately) by drawing rectangles.
- The definite integral of a function can be shown as the area of the region bounded by its graph of the given function between two points in the line.
- The area of a region is found by splitting it into thin vertical rectangles and applying the lower and the upper limits, the area of the region is summarized.
- An integral of a function over an interval on which the integral is described.
Also, F(x) is known to be a Newton-Leibnitz integral or antiderivative or primitive of a function f(x) on an interval I.
F'(x) = f(x)
For every value of x = I.
Types of Integrals:
Integral calculus helps to resolve two major types of problems:
- The problem of getting a function if its derivative is given.
- The problem of getting the area bounded by the graph of a function under given situations.