हिंदी

Determine the order and degree of the following differential equations. Solution D.E. y = 1 − logx x2d2ydx2=1 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Determine the order and degree of the following differential equations.

Solution D.E.
y = 1 − logx `x^2(d^2y)/dx^2 = 1`
योग
Advertisements

उत्तर

y = 1 – log x

Differentiating w.r.t. x, we get

`dy/dx = -1/x`

Again, differentiating w.r.t. x, we get

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

∴ `x^2(d^2y)/dx^2 = 1`

∴  Given function is a solution of the given differential equation.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Differential Equation and Applications - Exercise 8.1 [पृष्ठ १६२]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 8 Differential Equation and Applications
Exercise 8.1 | Q 2.4 | पृष्ठ १६२

संबंधित प्रश्न

Verify that y2 = 4ax is a solution of the differential equation y = x \[\frac{dy}{dx} + a\frac{dx}{dy}\]


Show that y = ax3 + bx2 + c is a solution of the differential equation \[\frac{d^3 y}{d x^3} = 6a\].

 


\[\frac{dy}{dx} - x \sin^2 x = \frac{1}{x \log x}\]

\[\sin^4 x\frac{dy}{dx} = \cos x\]

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

x cos y dy = (xex log x + ex) dx


Solve the following differential equation: 
(xy2 + 2x) dx + (x2 y + 2y) dy = 0


Solve the following differential equation:
\[xy\frac{dy}{dx} = 1 + x + y + xy\]

 


\[\frac{dr}{dt} = - rt, r\left( 0 \right) = r_0\]

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


In a bank principal increases at the rate of r% per year. Find the value of r if ₹100 double itself in 10 years (loge 2 = 0.6931).


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

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given the number triples in 5 hrs, find how many bacteria will be present after 10 hours. Also find the time necessary for the number of bacteria to be 10 times the number of initial present.


In a simple circuit of resistance R, self inductance L and voltage E, the current `i` at any time `t` is given by L \[\frac{di}{dt}\]+ R i = E. If E is constant and initially no current passes through the circuit, prove that \[i = \frac{E}{R}\left\{ 1 - e^{- \left( R/L \right)t} \right\}.\]


Find the equation of the curve such that the portion of the x-axis cut off between the origin and the tangent at a point is twice the abscissa and which passes through the point (1, 2).


Which of the following is the integrating factor of (x log x) \[\frac{dy}{dx} + y\] = 2 log x?


Verify that the function y = e−3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + \frac{dy}{dx} - 6y = 0.\]


Choose the correct option from the given alternatives:

The solution of `1/"x" * "dy"/"dx" = tan^-1 "x"` is


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.


Solve the following differential equation.

`(x + y) dy/dx = 1`


Solve the following differential equation.

`dy/dx + 2xy = x`


A solution of a differential equation which can be obtained from the general solution by giving particular values to the arbitrary constants is called ___________ solution.


Solve the differential equation:

`e^(dy/dx) = x`


Solve the following differential equation `("d"y)/("d"x)` = x2y + y


Solve: `("d"y)/("d"x) = cos(x + y) + sin(x + y)`. [Hint: Substitute x + y = z]


There are n students in a school. If r % among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?


`d/(dx)(tan^-1  (sqrt(1 + x^2) - 1)/x)` is equal to:


Solve the differential equation

`y (dy)/(dx) + x` = 0


Solve the differential equation `dy/dx + xy = xy^2` and find the particular solution when y = 4, x = 1.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×