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

Choose the correct alternative: Solution of the equation ddxdydx = y log y is - Mathematics and Statistics

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प्रश्न

Choose the correct alternative:

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

पर्याय

  • y = aex 

  • y = be2x 

  • y = be–2x 

  • y = eax

MCQ
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उत्तर

y = eax

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.8: Differential Equation and Applications - Q.1

संबंधित प्रश्‍न

\[\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 + xy = 0\]

Show that the function y = A cos 2x − B sin 2x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 4y = 0\].


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

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

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

Differential equation Function
\[x\frac{dy}{dx} = y\]
y = ax

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

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

x cos2 y  dx = y cos2 x dy


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

\[\frac{dy}{dx} = 2 e^{2x} y^2 , y\left( 0 \right) = - 1\]

Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\]  given that y = 1, when x = 0.


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

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

2xy dx + (x2 + 2y2) dy = 0


Solve the following differential equations:
\[\frac{dy}{dx} = \frac{y}{x}\left\{ \log y - \log x + 1 \right\}\]


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

Solve the following initial value problem:-

\[\frac{dy}{dx} + y \tan x = 2x + x^2 \tan x, y\left( 0 \right) = 1\]


A population grows at the rate of 5% per year. How long does it take for the population to double?


The differential equation \[x\frac{dy}{dx} - y = x^2\], has the general solution


Integrating factor of the differential equation cos \[x\frac{dy}{dx} + y \sin x = 1\], is


Which of the following differential equations has y = C1 ex + C2 ex as the general solution?


Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.


Find the equation of the plane passing through the point (1, -2, 1) and perpendicular to the line joining the points A(3, 2, 1) and B(1, 4, 2). 


Choose the correct option from the given alternatives:

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


In the following example, verify that the given function is a solution of the corresponding differential equation.

Solution D.E.
y = xn `x^2(d^2y)/dx^2 - n xx (xdy)/dx + ny =0`

Solve the following differential equation.

`dy/dx + y` = 3


Solve the following differential equation.

dr + (2r)dθ= 8dθ


Solve the differential equation `("d"y)/("d"x) + y` = e−x 


Solve the following differential equation y log y = `(log  y - x) ("d"y)/("d"x)`


The function y = cx is the solution of differential equation `("d"y)/("d"x) = y/x`


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


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


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