F(x, y) = ycos(yx)+xxcos(yx) is not a homogeneous function.

F(x, y) = `(ycos(y/x) + x)/(xcos(y/x))` is not a homogeneous function.

MCQ

True or False

This statement is True.

Explanation:

Because f(λx, λy) = λ°f(x, y).

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Chapter 9: Differential Equations - Solved Examples [Page 191]

Chapter 9 Differential Equations
Solved Examples | Q 23. (iv) | Page 191

Solve the differential equation (x² + y²)dx- 2xydy = 0

Show that the differential equation `2xydy/dx=x^2+3y^2` is homogeneous and solve it.

Find the particular solution of the differential equation:

2y e^x/y dx + (y - 2x e^x/y) dy = 0 given that x = 0 when y = 1.

Show that the given differential equation is homogeneous and solve them.

`x^2 dy/dx = x^2 - 2y^2 + xy`

For the differential equation find a particular solution satisfying the given condition:

(x + y) dy + (x – y) dx = 0; y = 1 when x = 1

For the differential equation find a particular solution satisfying the given condition:

x² dy + (xy + y²) dx = 0; y = 1 when x = 1

For the differential equation find a particular solution satisfying the given condition:

`dy/dx - y/x + cosec (y/x) = 0; y = 0` when x = 1

For the differential equation find a particular solution satisfying the given condition:

`2xy + y^2 - 2x^2 dy/dx = 0; y = 2` when x = 1

Find the particular solution of the differential equation `(x - y) dy/dx = (x + 2y)` given that y = 0 when x = 1.

(x² − 2xy) dy + (x² − 3xy + 2y²) dx = 0

(x² + 3xy + y²) dx − x² dy = 0

(2x² y + y³) dx + (xy² − 3x³) dy = 0

Solve the following initial value problem:
(x² + y²) dx = 2xy dy, y (1) = 0

Solve the following initial value problem:
(y⁴ − 2x³ y) dx + (x⁴ − 2xy³) dy = 0, y (1) = 1

Find the particular solution of the differential equation \[\left( x - y \right)\frac{dy}{dx} = x + 2y\], given that when x = 1, y = 0.

Solve the differential equation: ` (dy)/(dx) = (x + y )/ (x - y )`

Solve the differential equation: x dy - y dx = `sqrt(x^2 + y^2)dx,` given that y = 0 when x = 1.