हिंदी

Which of the Following Differential Equations Has Y = C1 Ex + C2 E–X as the General Solution? - Mathematics

Advertisements
Advertisements

प्रश्न

Which of the following differential equations has y = c1 ex + c2 e–x as the general solution?

(A) `(d^2y)/(dx^2) + y = 0`

(B) `(d^2y)/(dx^2) - y = 0`

(C) `(d^2y)/(dx^2) + 1 = 0`

(D) `(d^2y)/(dx^2)  - 1 = 0`

 

 

Advertisements

उत्तर

This is the required differential equation of the given equation of curve.

Hence, the correct answer is B.

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 11 | पृष्ठ ३९१

संबंधित प्रश्न

Form the differential equation of the family of ellipses having foci on y-axis and centre at origin.


Which of the following differential equation has y = x as one of its particular solution?

A. `(d^2y)/(dx^2) - x^2 (dy)/(dx) + xy = x`

B. `(d^2y)/(dx^2) + x dy/dx + xy = x`

C. `(d^2y)/(dx^2) - x^2 dy/dx + xy = 0`

D. `(d^2y)/(dx^2) + x dy/dx + xy = 0`

 

 

 


For the curve y = 5x – 2x3, if x increases at the rate of 2 units/sec, then find the rate of change of the slope of the curve when x = 3


Form the differential equation of the family of curves represented by y2 = (x − c)3.


Form the differential equation corresponding to y = emx by eliminating m.


Form the differential equation corresponding to (x − a)2 + (y − b)2 = r2 by eliminating a and b.


Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x2 − y2 = a2


Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.


Find one-parameter families of solution curves of the following differential equation:-

\[\frac{dy}{dx} + 3y = e^{mx}\], m is a given real number.


Find one-parameter families of solution curves of the following differential equation:-

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


Find one-parameter families of solution curves of the following differential equation:-

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


Find one-parameter families of solution curves of the following differential equation:-

\[\left( x + y \right)\frac{dy}{dx} = 1\]


Find one-parameter families of solution curves of the following differential equation:-

\[x \log x\frac{dy}{dx} + y = 2 \log x\]


Write the order of the differential equation representing the family of curves y = ax + a3.


The differential equation which represents the family of curves y = eCx is


Form the differential equation representing the family of curves y = mx, where m is an arbitrary constant.


Form the differential equation of the family of ellipses having foci on y-axis and centre at the origin.


Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.


Form the differential equation representing the family of curves `y2 = m(a2 - x2) by eliminating the arbitrary constants 'm' and 'a'. 


Form the differential equation representing the family of curves y = e2x (a + bx), where 'a' and 'b' are arbitrary constants.


Form the differential equation representing the family of curves y = A sin x, by eliminating the arbitrary constant A.


Find the differential equation of the family of lines through the origin.


The differential equation representing the family of curves y = A sinx + B cosx is ______.


Find the equation of a curve passing through origin and satisfying the differential equation `(1 + x^2) "dy"/"dx" + 2xy` = 4x2 


Find the equation of the curve through the point (1, 0) if the slope of the tangent to the curve at any point (x, y) is `(y - 1)/(x^2 + x)`


Find the equation of a curve passing through origin if the slope of the tangent to the curve at any point (x, y) is equal to the square of the difference of the abcissa and ordinate of the point.


Family y = Ax + A3 of curves is represented by the differential equation of degree ______.


The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.


The differential equation of the family of curves x2 + y2 – 2ay = 0, where a is arbitrary constant, is ______.


The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is ______.


The differential equation of the family of curves y2 = 4a(x + a) is ______.


Differential equation representing the family of curves y = ex (Acosx + Bsinx) is `("d"^2y)/("d"x^2) - 2 ("d"y)/("d"x) + 2y` = 0


The area above the x-axis and under the curve `y = sqrt(1/x - 1)` for `1/2 ≤ x ≤ 1` is:


Form the differential equation of family of circles having centre on y-axis and raduis 3 units


Form the differential equation of the family of hyperbola having foci on x-axis and centre at origin.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×