Assertion (A): dy/dx = (x^2 + y^2)/x^2 is a homogeneous differential equation. Reason (R): Every equation dy/dx = F(x, y) with F a ratio of two polynomials is homogeneous.

Question 39

MediumOriginal question

Assertion (A): $\frac{dy}{dx} = \frac{x^{2} + y^{2}}{x^{2}}$ is a homogeneous differential equation.
Reason (R): Every equation $\frac{dy}{dx} = F(x, y)$ with $F$ a ratio of two polynomials is homogeneous.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A is true: $F = 1 + \left(\frac{y}{x}\right)^{2}$ , a function of $\frac{y}{x}$ , degree 0.
R is false: $\frac{x + y + 1}{x - y}$ is a ratio of polynomials but not homogeneous.

Concept: Which equations are homogeneous
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsSolving homogeneous equations

Practise this chapter →

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Assertion (A): dydx=x2+y2x2\frac{dy}{dx} = \frac{x^{2} + y^{2}}{x^{2}}dxdy​=x2x2+y2​ is a homogeneous differential equation.Reason (R): Every equation dydx=F(x,y)\frac{dy}{dx} = F(x, y)dxdy​=F(x,y) with FFF a ratio of two polynomials is homogeneous.

Explanation

Assertion (A): $\frac{dy}{dx} = \frac{x^{2} + y^{2}}{x^{2}}$ is a homogeneous differential equation.
Reason (R): Every equation $\frac{dy}{dx} = F(x, y)$ with $F$ a ratio of two polynomials is homogeneous.