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

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.

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प्रश्न

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.

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उत्तर

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

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 8: Differential Equation and Applications - Miscellaneous Exercise 8 [पृष्ठ १७२]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 2.3 | पृष्ठ १७२

संबंधित प्रश्‍न

Assume that a rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.

 

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


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

Differential equation Function
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\[y = ax + b + \frac{1}{2x}\]

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

xy (y + 1) dy = (x2 + 1) dx


(1 + x) (1 + y2) dx + (1 + y) (1 + x2) dy = 0


y (1 + ex) dy = (y + 1) ex dx


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

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

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\[\left[ x\sqrt{x^2 + y^2} - y^2 \right] dx + xy\ dy = 0\]

If the interest is compounded continuously at 6% per annum, how much worth Rs 1000 will be after 10 years? How long will it take to double Rs 1000?


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Choose the correct option from the given alternatives:

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Solution D.E.
ax2 + by2 = 5 `xy(d^2y)/dx^2+ x(dy/dx)^2 = y dy/dx`

Solve the following differential equation.

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


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y2 dx + (xy + x2)dy = 0


Select and write the correct alternative from the given option for the question

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What distinguishes an ordinary differential equation from other types of differential equations?


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