हिंदी

( D Y D X ) 2 + 1 D Y / D X = 2

Advertisements
Advertisements

प्रश्न

\[\left( \frac{dy}{dx} \right)^2 + \frac{1}{dy/dx} = 2\]
एक पंक्ति में उत्तर
योग
Advertisements

उत्तर

\[\left( \frac{dy}{dx} \right)^2 + \frac{1}{\left( \frac{dy}{dx} \right)} = 2\]

\[\Rightarrow \frac{\left( \frac{dy}{dx} \right)^3 + 1}{\left( \frac{dy}{dx} \right)} = 2\]
\[\Rightarrow \left( \frac{dy}{dx} \right)^3 - 2\frac{dy}{dx} + 1 = 0\]
In this equation, the order of the highest order derivative is 1 and its highest power is 3. So, it is a differential equation of order 1 and degree 3.
It is a non-linear differential equation because the differential coefficient \[\frac{dy}{dx}\]  has exponent 3, which is greater than 1.
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 3 | पृष्ठ ५

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

For the following differential equation verify that the accompanying function is a solution:

Differential equation Function
\[x + y\frac{dy}{dx} = 0\]
\[y = \pm \sqrt{a^2 - x^2}\]

Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 0, y' \left( 0 \right) = 1\] Function y = sin x


Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 1\] Function y = sin x + cos x


\[\left( x + 2 \right)\frac{dy}{dx} = x^2 + 3x + 7\]

\[\left( x^3 + x^2 + x + 1 \right)\frac{dy}{dx} = 2 x^2 + x\]

\[5\frac{dy}{dx} = e^x y^4\]

\[x\frac{dy}{dx} + \cot y = 0\]

\[\frac{dy}{dx} = e^{x + y} + e^y x^3\]

\[\sqrt{1 + x^2} dy + \sqrt{1 + y^2} dx = 0\]

\[\frac{dy}{dx} = 1 + x + y^2 + x y^2\] when y = 0, x = 0

Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]


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

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

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

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

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

Find the particular solution of the differential equation \[\frac{dy}{dx} = \frac{xy}{x^2 + y^2}\] given that y = 1 when x = 0.

 


Solve the following initial value problem:-
\[\tan x\left( \frac{dy}{dx} \right) = 2x\tan x + x^2 - y; \tan x \neq 0\] given that y = 0 when \[x = \frac{\pi}{2}\]


Find the equation of the curve which passes through the point (2, 2) and satisfies the differential equation
\[y - x\frac{dy}{dx} = y^2 + \frac{dy}{dx}\]


The integrating factor of the differential equation (x log x)
\[\frac{dy}{dx} + y = 2 \log x\], is given by


The differential equation satisfied by ax2 + by2 = 1 is


Which of the following transformations reduce the differential equation \[\frac{dz}{dx} + \frac{z}{x}\log z = \frac{z}{x^2} \left( \log z \right)^2\] into the form \[\frac{du}{dx} + P\left( x \right) u = Q\left( x \right)\]


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

`y=sqrt(a^2-x^2)`              `x+y(dy/dx)=0`


Find the particular solution of the differential equation `"dy"/"dx" = "xy"/("x"^2+"y"^2),`given that y = 1 when x = 0


Determine the order and degree of the following differential equations.

Solution D.E
y = aex + be−x `(d^2y)/dx^2= 1`

Form the differential equation from the relation x2 + 4y2 = 4b2


Solve the following differential equation.

`dy/dx = x^2 y + y`


For the following differential equation find the particular solution.

`(x + 1) dy/dx − 1 = 2e^(−y)`,

when y = 0, x = 1


For each of the following differential equations find the particular solution.

`y (1 + logx)dx/dy - x log x = 0`,

when x=e, y = e2.


The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.


Choose the correct alternative.

The integrating factor of `dy/dx -  y = e^x `is ex, then its solution is


x2y dx – (x3 + y3) dy = 0


Choose the correct alternative:

General solution of `y - x ("d"y)/("d"x)` = 0 is


Find the particular solution of the following differential equation

`("d"y)/("d"x)` = e2y cos x, when x = `pi/6`, y = 0.

Solution: The given D.E. is `("d"y)/("d"x)` = e2y cos x

∴ `1/"e"^(2y)  "d"y` = cos x dx

Integrating, we get

`int square  "d"y` = cos x dx

∴ `("e"^(-2y))/(-2)` = sin x + c1

∴ e–2y = – 2sin x – 2c1

∴ `square` = c, where c = – 2c1 

This is general solution.

When x = `pi/6`, y = 0, we have

`"e"^0 + 2sin  pi/6` = c

∴ c = `square`

∴ particular solution is `square`


Given that `"dy"/"dx" = "e"^-2x` and y = 0 when x = 5. Find the value of x when y = 3.


lf the straight lines `ax + by + p` = 0 and `x cos alpha + y sin alpha = p` are inclined at an angle π/4 and concurrent with the straight line `x sin alpha - y cos alpha` = 0, then the value of `a^2 + b^2` is


A man is moving away from a tower 41.6 m high at a rate of 2 m/s. If the eye level of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower, is


Which of the following is an example of an ordinary differential equation?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×