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Define a Differential Equation.

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प्रश्न

Define a differential equation.

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उत्तर

Differential equation:
An equation containing an independent variable, a dependent variable and differential coefficients of the dependent variable with respect to the independent variable is called a differential equation.
for example: \[\frac{dy}{dx} = e^{x + y}\]

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अध्याय 21: Differential Equations - Very Short Answers [पृष्ठ १३७]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 21 Differential Equations
Very Short Answers | Q 1 | पृष्ठ १३७

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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

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


Show that y = ex (A cos x + B sin x) is the solution of the differential equation \[\frac{d^2 y}{d x^2} - 2\frac{dy}{dx} + 2y = 0\]


Verify that y = log \[\left( x + \sqrt{x^2 + a^2} \right)^2\]  satisfies the differential equation \[\left( a^2 + x^2 \right)\frac{d^2 y}{d x^2} + x\frac{dy}{dx} = 0\]


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Differential equation Function
\[y = \left( \frac{dy}{dx} \right)^2\]
\[y = \frac{1}{4} \left( x \pm a \right)^2\]

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

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

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

\[\frac{dy}{dx} = 2 e^x y^3 , y\left( 0 \right) = \frac{1}{2}\]

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Find the particular solution of edy/dx = x + 1, given that y = 3, when x = 0.


Find the particular solution of the differential equation
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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.


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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.


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State whether the following statement is True or False:

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