हिंदी

D Y D X + E Y = 0

Advertisements
Advertisements

प्रश्न

\[\frac{dy}{dx} + e^y = 0\]
एक पंक्ति में उत्तर
योग
Advertisements

उत्तर

\[\frac{dy}{dx} + e^y = 0\]

In this differential equation, the order of the highest order derivative is 1 and its power is 1. So, the order of the differential equation is 1 and its degree is 1.

It is a non-linear differential equation, as the exponent of the dependent variable is not equal to 1 (as per expansion series of \[e^y\]).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 21: Differential Equations - Exercise 22.01 [पृष्ठ ५]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 21 Differential Equations
Exercise 22.01 | Q 25 | पृष्ठ ५

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Write the degree of the differential equation `x^3((d^2y)/(dx^2))^2+x(dy/dx)^4=0`


Order and degree of the differential equation `[1+(dy/dx)^3]^(7/3)=7(d^2y)/(dx^2)` are respectively 

(A) 2, 3

(B) 3, 2

(C) 7, 2

(D) 3, 7


Determine the order and degree (if defined) of the differential equation:

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


For the given below, verify that the given function (implicit or explicit) is a solution to the corresponding differential equation.

`y = xsin 3x   :   (d^2y)/(dx^2) + 9y - 6 cos 3x = 0`


\[e^\frac{dy}{dx} = x + 1 ; y\left( 0 \right) = 3\]

Define degree of a differential equation.


Write the degree of the differential equation
\[\frac{d^2 y}{d x^2} + x \left( \frac{dy}{dx} \right)^2 = 2 x^2 \log \left( \frac{d^2 y}{d x^2} \right)\]


Write the degree of the differential equation \[\left( \frac{dy}{dx} \right)^4 + 3x\frac{d^2 y}{d x^2} = 0\]


Write the degree of the differential equation \[x^3 \left( \frac{d^2 y}{d x^2} \right)^2 + x \left( \frac{dy}{dx} \right)^4 = 0\]


The order of the differential equation satisfying
\[\sqrt{1 - x^4} + \sqrt{1 - y^4} = a\left( x^2 - y^2 \right)\] is


Determine the order and degree (if defined) of the following differential equation:-

y"' + y2 + ey' = 0


In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = cos x + C            y' + sin x = 0


Find the order and the degree of the differential equation `x^2 (d^2y)/(dx^2) = { 1 + (dy/dx)^2}^4`


Determine the order and degree of the following differential equation:

`root(3)(1 +("dy"/"dx")^2) = ("d"^2"y")/"dx"^2`


Determine the order and degree of the following differential equation:

`(dy)/(dx) = (2sin x + 3)/(dy/dx)`


Determine the order and degree of the following differential equation:

(y''')2 + 3y'' + 3xy' + 5y = 0


Determine the order and degree of the following differential equation:

`(("d"^3"y")/"dx"^3)^(1/2) - ("dy"/"dx")^(1/3) = 20`


Determine the order and degree of the following differential equation:

`"x" + ("d"^2"y")/"dx"^2 = sqrt(1 + (("d"^2"y")/"dx"^2)^2)`


Determine the order and degree of the following differential equation:

`"dy"/"dx" = 3"y" + root(4)(1 + 5 ("dy"/"dx")^2)`


Determine the order and degree of the following differential equations.

`((d^3y)/dx^3)^(1/6) = 9`


State whether the following statement is true or false:

Order and degree of a differential equation are always positive integers.


Select and write the correct alternative from the given option for the question

The order and degree of `(("d"y)/("d"x))^3 - ("d"^3y)/("d"x^3) + y"e"^x` = 0 are respectively


Order and degree of differential equation are always ______ integers


Order and degree of differential equation`(("d"^3y)/("d"x^3))^(1/6)`= 9 is ______


The order and degree of the differential equation `[1 + ["dy"/"dx"]^3]^(7/3) = 7 (("d"^2"y")/"dx"^2)` are respectively.


The third order differential equation is ______ 


The order and degree of `(("n + 1")/"n")("d"^4"y")/"dx"^4 = ["n" + (("d"^2"y")/"dx"^2)^4]^(3//5)` are respectively.


The degree of the differential equation `(("d"^2y)/("d"x^2))^2 + (("d"y)/("d"x))^2 = xsin(("d"y)/("d"x))` is ______.


The degree of the differential equation `[1 + (("d"y)/("d"x))^2]^(3/2) = ("d"^2y)/("d"x^2)` is ______.


The order and degree of the differential equation `(("d"^3y)/("d"x^3))^2 - 3 ("d"^2y)/("d"x^2) + 2(("d"y)/("d"x))^4` = y4 are ______.


The degree of the differential equation `("d"^2y)/("d"x^2) + "e"^((dy)/(dx))` = 0 is ______.


y2 = (x + c)3 is the general solution of the differential equation ______.


The order and degree of the differential equation `sqrt(dy/dx) - 4 dy/dx - 7x` = 0 are ______.


The degree of the differential equation `[1 + (dy/dx)^2]^3 = ((d^2y)/(dx^2))^2` is ______.


Find the order and degree of the differential equation `(d^2y)/(dx^2) = root(3)(1 - (dy/dx)^4`


The degree of the differential equation `((d^3y)/(dx^2))^4 + ((d^2y)/(dx^2))^5 + (dy)/(dx) + y = 0` is ______.


For the differential equation \[y''' + y^{2} + e^{y'} = 0\], what is the order?


Which of the following statements is true regarding order and degree of differential equations?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×