हिंदी

सी. बी. एस. ई.वाणिज्य (अंग्रेजी माध्यम) कक्षा १२

प्रश्न पत्र

प्रश्न पत्र२४८९

पाठ्यपुस्तक उत्तर२०२१६

MCQ ऑनलाइन अभ्यास परीक्षा४२

महत्वपूर्ण प्रश्न एवं उत्तर१८८७३

अवधारणा स्पष्टीकरण और वीडियो२४२

समय सारणी२३

पाठ्यक्रम

F(x, y) = x2+y2+yx is a homogeneous function of degree ______. - Mathematics

Advertisements

Advertisements

प्रश्न

F(x, y) = $\frac{\sqrt{x^{2} + y^{2}} + y}{x}$ is a homogeneous function of degree ______.

रिक्त स्थान भरें

उत्तर

F(x, y) = $\frac{\sqrt{x^{2} + y^{2}} + y}{x}$ is a homogeneous function of degree Zero.

shaalaa.com

Methods of Solving First Order, First Degree Differential Equations - Homogeneous Differential Equations

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 22. (iv)Q 22. (iii)Q 22. (v)

अध्याय 9: Differential Equations - Solved Examples [पृष्ठ १८९]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12

अध्याय 9 Differential Equations
Solved Examples | Q 22. (iv) | पृष्ठ १८९

वीडियो ट्यूटोरियलVIEW ALL [3]

view
वीडियो ट्यूटोरियल For All Subjects
Methods of Solving First Order, First Degree Differential Equations - Homogeneous Differential Equations

video tutorial00:26:29
Methods of Solving First Order, First Degree Differential Equations - Homogeneous Differential Equations

video tutorial00:30:13
Methods of Solving First Order, First Degree Differential Equations - Homogeneous Differential Equations

video tutorial00:38:44

संबंधित प्रश्न

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

$y' = \frac{x + y}{x}$

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

(x² – y²) dx + 2xy dy = 0

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

$x d y - y d x = \sqrt{x^{2} + y^{2}} d x$

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

${x \cos (\frac{y}{x}) + y \sin (\frac{y}{x})} y d x = {y \sin (\frac{y}{x}) - x \cos (\frac{y}{x})} x d y$

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

$x \frac{d y}{d x} - y + x \sin (\frac{y}{x}) = 0$

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

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

A homogeneous differential equation of the from $\frac{d x}{d y} = h (\frac{x}{y})$ can be solved by making the substitution.

Find the particular solution of the differential equation $(x - y) \frac{d y}{d x} = (x + 2 y)$ given that y = 0 when x = 1.

Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x³ – 3xy²)dx = (y³ – 3x²y)dy, where C is parameter

x \frac{d y}{d x} - y = 2 \sqrt{y^{2} - x^{2}}

x \cos (\frac{y}{x}) \cdot (y d x + x d y) = y \sin (\frac{y}{x}) \cdot (x d y - y d x)

(x - y) \frac{d y}{d x} = x + 2 y

(2x² y + y³) dx + (xy² − 3x³) dy = 0

y d x + {x \log (\frac{y}{x})} d y - 2 x d y = 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

Show that the family of curves for which $\frac{d y}{d x} = \frac{x^{2} + y^{2}}{2 x y}$ , is given by $x^{2} - y^{2} = C x$

Which of the following is a homogeneous differential equation?

Solve the following differential equation : $[y - x \cos (\frac{y}{x})] d y + [y \cos (\frac{y}{x}) - 2 x \sin (\frac{y}{x})] d x = 0$ .

Solve the following differential equation:

$(1 + 2 e^{\frac{x}{y}}) + 2 e^{\frac{x}{y}} (1 - \frac{x}{y}) \frac{dy}{dx} = 0$

Solve the following differential equation:

y² dx + (xy + x²)dy = 0

Solve the following differential equation:

$y^{2} - x^{2} \frac{dy}{dx} = xy \frac{dy}{dx}$

F(x, y) = $\frac{y \cos (\frac{y}{x}) + x}{x \cos (\frac{y}{x})}$ is not a homogeneous function.

A homogeneous differential equation of the $\frac{d x}{d y} = h (\frac{x}{y})$ can be solved by making the substitution.

If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation, 2x²dy = (2xy + y²)dx, then $f (\frac{1}{2})$ is equal to ______.

Read the following passage:

An equation involving derivatives of the dependent variable with respect to the independent variables is called a differential equation. A differential equation of the form $\frac{d y}{d x}$ = F(x, y) is said to be homogeneous if F(x, y) is a homogeneous function of degree zero, whereas a function F(x, y) is a homogeneous function of degree n if F(λx, λy) = λⁿ F(x, y).

To solve a homogeneous differential equation of the type $\frac{d y}{d x}$ = F(x, y) = $g (\frac{y}{x})$ , we make the substitution y = vx and then separate the variables.

Based on the above, answer the following questions:

Show that (x² – y²) dx + 2xy dy = 0 is a differential equation of the type $\frac{d y}{d x} = g (\frac{y}{x})$ . (2)
Solve the above equation to find its general solution. (2)

Notifications

English हिंदी मराठी

Login

Create free account

Course

वाणिज्य (अंग्रेजी माध्यम) कक्षा १२ सी. बी. एस. ई.

Change mode
Log out

Select a course

Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.