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

The function y = ex is solution ______ of differential equation - Mathematics and Statistics

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प्रश्न

The function y = ex is solution  ______ of differential equation

रिकाम्या जागा भरा

उत्तर

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

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.8: Differential Equation and Applications - Q.2

संबंधित प्रश्‍न

Verify that y = − x − 1 is a solution of the differential equation (y − x) dy − (y2 − x2) dx = 0.


\[\frac{dy}{dx} = \tan^{- 1} x\]


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

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

xy (y + 1) dy = (x2 + 1) dx


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

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

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

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

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

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

Solve the following initial value problem:-
\[x\frac{dy}{dx} - y = \log x, y\left( 1 \right) = 0\]


The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time t.


Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y + 2 (x + 1) = 2e2x.


Find the equation of the curve which passes through the origin and has the slope x + 3y− 1 at any point (x, y) on it.


If xmyn = (x + y)m+n, prove that \[\frac{dy}{dx} = \frac{y}{x} .\]


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


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


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


Solution of `x("d"y)/("d"x) = y + x tan  y/x` is `sin(y/x)` = cx


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