Which of the following is not a homogeneous function of x and y. - Mathematics

प्रश्न

Which of the following is not a homogeneous function of x and y.

विकल्प

x² + 2xy
2x – y
`cos^2 (y/x) + y/x`
sinx – cosy

MCQ

उत्तर

sinx – cosy

shaalaa.com

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

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 19 Q 18 Q 20

अध्याय 9: Differential Equations - Solved Examples [पृष्ठ १८८]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12

अध्याय 9 Differential Equations
Solved Examples | Q 19 | पृष्ठ १८८

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 differential equation 2y^x^/y dx + (y − 2x e^x/^y) dy = 0 is homogeneous. Find the particular solution of this differential equation, given that x = 0 when y = 1.

Solve the differential equation :

`y+x dy/dx=x−y dy/dx`

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 dy - y dx = sqrt(x^2 + y^2) dx`

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:

`[xsin^2(y/x - y)] dx + x dy = 0; y = pi/4 "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

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

\[\frac{y}{x}\cos\left( \frac{y}{x} \right) dx - \left\{ \frac{x}{y}\sin\left( \frac{y}{x} \right) + \cos\left( \frac{y}{x} \right) \right\} dy = 0\]

\[\left( 1 + e^{x/y} \right) dx + e^{x/y} \left( 1 - \frac{x}{y} \right) dy = 0\]

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

\[x\frac{dy}{dx} = y - x \cos^2 \left( \frac{y}{x} \right)\]

\[x\frac{dy}{dx} - y = 2\sqrt{y^2 - x^2}\]

\[\left( x - y \right)\frac{dy}{dx} = x + 2y\]

(2x² y + y³) dx + (xy² − 3x³) dy = 0

\[x\frac{dy}{dx} - y + x \sin\left( \frac{y}{x} \right) = 0\]

\[y dx + \left\{ x \log\left( \frac{y}{x} \right) \right\} dy - 2x dy = 0\]

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

Which of the following is a homogeneous differential equation?

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

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