State whether the following statement is True or False: A homogeneous differential equation is solved by substituting y = vx and integrating it

State whether the following statement is True or False:

A homogeneous differential equation is solved by substituting y = vx and integrating it

MCQ

True or False

True

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Chapter 1.8: Differential Equation and Applications - Q.3

Chapter 1.8 Differential Equation and Applications
Q.3 | Q 6

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

(x² + xy) dy = (x² + y²) dx

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

`y' = (x + y)/x`

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

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

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

`y dx + x log(y/x)dy - 2x dy = 0`

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

Solve the following initial value problem:
\[\frac{dy}{dx} - \frac{y}{x} + cosec\frac{y}{x} = 0, y\left( 1 \right) = 0\]

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

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

Solve the following initial value problem:
x (x² + 3y²) dx + y (y² + 3x²) dy = 0, y (1) = 1

Solve the following initial value problem:
\[x\frac{dy}{dx} - y + x \sin\left( \frac{y}{x} \right) = 0, y\left( 2 \right) = x\]

Show that the family of curves for which \[\frac{dy}{dx} = \frac{x^2 + y^2}{2xy}\], is given by \[x^2 - y^2 = Cx\]

Which of the following is a homogeneous differential equation?

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