# Solution of a differential equation \[xdy - ydx = 0\] represents

A. A rectangular hyperbola

B. Parabola whose vertex is at origin

C. Straight line passing through origin

D. A circle whose center is at origin

Answer

Verified

279.6k+ views

**Hint:**Given is the solution of a differential equation. We need to find that equation. So we will separate the variable or function with its respective derivative term.Then we will integrate the equation. After integrating we will definitely get the perfect answer.

**Complete step by step answer:**

Given is the solution of a differential equation,

\[xdy - ydx = 0\]

Separating the variables,

\[xdy = ydx\]

Now separating the respective variables,

\[\dfrac{{dy}}{y} = \dfrac{{dx}}{x}\]

Integrating both sides we get,

\[\int {\dfrac{{dy}}{y} = \int {\dfrac{{dx}}{x}} } \]

Taking the integral we get,

\[\log y = \log x + \log C\]

Removing the log on both the sides,

\[\therefore y = xC\]

This is the respective equation. Thus we know that is the equation of a straight line that passes through the origin.

**Thus option C is the correct answer.**

**Note:**In order to get the correct answer as we did the process above. But we should know that equation of all other options so that it becomes easy to tick the correct answer. Since all the geometrical shapes are having either vertex or center on the origin we should not miss a single step.

-Rectangular hyperbola \[xy = {C^2}\]

-Parabola with vertex at origin \[{y^2} = 4ax\]

-Circle with centre is at origin \[{x^2} + {y^2} = {r^2}\]

Recently Updated Pages

Define absolute refractive index of a medium

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Scroll valve is present in a Respiratory system of class 11 biology CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

is known as the Land of the Rising Sun A Japan B Norway class 8 social science CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE