हिंदी

Form a Differential Equation Representing the Given Family of Curves by Eliminating Arbitrary Constants a and B. Y = E2x (A + Bx) - Mathematics

Advertisements
Advertisements

प्रश्न

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

y = e2x (a + bx)

Advertisements

उत्तर

y = e2x (a + bx) ...(1)

Differentiating both sides with respect to x, we get:

This is the required differential equation of the given curve.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differential Equations - Exercise 9.3 [पृष्ठ ३९१]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 9 Differential Equations
Exercise 9.3 | Q 4 | पृष्ठ ३९१

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Write the integrating factor of the following differential equation:

(1+y2) dx(tan1 yx) dy=0


Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.


Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

`x/a + y/b = 1`


Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

y = ex (a cos x + b sin x)


Solve the differential equation  `ye^(x/y) dx = (xe^(x/y) + y^2)dy, (y != 0)`


Find a particular solution of the differential equation (x - y) (dx + dy) = dx - dy, given that y = -1, when x = 0. (Hint: put x - y = t)


The general solution of the differential equation `(y dx - x dy)/y = 0` is ______.


Find the differential equation representing the family of curves `y = ae^(bx + 5)`. where a and b are arbitrary constants.


The equation of the curve satisfying the differential equation y (x + y3) dx = x (y3 − x) dy and passing through the point (1, 1) is


Verify that xy = a ex + b ex + x2 is a solution of the differential equation \[x\frac{d^2 y}{d x^2} + 2\frac{dy}{dx} - xy + x^2 - 2 = 0.\]


Show that y2 − x2 − xy = a is a solution of the differential equation \[\left( x - 2y \right)\frac{dy}{dx} + 2x + y = 0.\]


Verify that y = A cos x + sin x satisfies the differential equation \[\cos x\frac{dy}{dx} + \left( \sin x \right)y=1.\]


Find the differential equation corresponding to y = ae2x + be3x + cex where abc are arbitrary constants.


\[\frac{dy}{dx} = \sin^3 x \cos^4 x + x\sqrt{x + 1}\]


\[\frac{dy}{dx} = x^2 e^x\]


\[(\tan^2 x + 2\tan x + 5)\frac{dy}{dx} = 2(1+\tan x)\sec^2x\]


\[\frac{dy}{dx} = \sin^3 x \cos^2 x + x e^x\]


tan y dx + tan x dy = 0


Solve the differential equation:

cosec3 x dy − cosec y dx = 0


The general solution of the differential equation `(dy)/(dx) + x/y` = 0 is


Solution of the equation 3 tan(θ – 15) = tan(θ + 15) is


The number of arbitrary constant in the general solution of a differential equation of fourth order are


Which of the following equations has `y = c_1e^x + c_2e^-x` as the general solution?


The general solution of the differential equation of the type `(dx)/(dy) + p_1y = theta_1` is


The general solution of the differential equation `x^xdy + (ye^x + 2x)  dx` = 0


Solve the differential equation: y dx + (x – y2)dy = 0


The general solution of the differential equation ydx – xdy = 0; (Given x, y > 0), is of the form

(Where 'c' is an arbitrary positive constant of integration)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×