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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution - Mathematics and Statistics

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प्रश्न

A solution of differential equation which can be obtained from the general solution by giving particular values to the arbitrary constant is called ______ solution

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उत्तर

particular

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पाठ 1.8: Differential Equation and Applications - Q.2

संबंधित प्रश्‍न

Show that the differential equation of which y = 2(x2 − 1) + \[c e^{- x^2}\] is a solution, is \[\frac{dy}{dx} + 2xy = 4 x^3\]


Show that y = AeBx is a solution of the differential equation

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

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


Show that Ax2 + By2 = 1 is a solution of the differential equation x \[\left\{ y\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 \right\} = y\frac{dy}{dx}\]

 


Differential equation \[x\frac{dy}{dx} = 1, y\left( 1 \right) = 0\]

Function y = log x


\[\sqrt{a + x} dy + x\ dx = 0\]

xy (y + 1) dy = (x2 + 1) dx


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

tan y \[\frac{dy}{dx}\] = sin (x + y) + sin (x − y) 

 


The volume of a spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of the balloon after `t` seconds.


Find the particular solution of the differential equation
(1 – y2) (1 + log x) dx + 2xy dy = 0, given that y = 0 when x = 1.


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

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

A bank pays interest by continuous compounding, that is, by treating the interest rate as the instantaneous rate of change of principal. Suppose in an account interest accrues at 8% per year, compounded continuously. Calculate the percentage increase in such an account over one year.


The differential equation obtained on eliminating A and B from y = A cos ωt + B sin ωt, is


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`


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

(x − y2 x) dx − (y + x2 y) dy = 0, when x = 2, y = 0


Solve the following differential equation.

xdx + 2y dx = 0


Solve the following differential equation.

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


Choose the correct alternative.

The differential equation of y = `k_1 + k_2/x` is


The integrating factor of the differential equation `dy/dx - y = x` is e−x.


Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`


Choose the correct alternative:

Solution of the equation `x("d"y)/("d"x)` = y log y is


The solution of differential equation `x^2 ("d"^2y)/("d"x^2)` = 1 is ______


Solve the following differential equation

`y log y ("d"x)/("d"y) + x` = log y


Solve: ydx – xdy = x2ydx.


Solve the differential equation `"dy"/"dx"` = 1 + x + y2 + xy2, when y = 0, x = 0.


The differential equation (1 + y2)x dx – (1 + x2)y dy = 0 represents a family of:


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