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

State whether the following is True or False: The degree of a differential equation is the power of the highest ordered derivative when all the derivatives are made free from negative

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प्रश्न

State whether the following is True or False:

The degree of a differential equation is the power of the highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
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उत्तर

The degree of a differential equation is the power of the highest ordered derivative when all the derivatives are made free from negative and/or fractional indices if any. - True

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

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 8 Differential Equation and Applications
Miscellaneous Exercise 8 | Q 3.3 | पृष्ठ १७२

संबंधित प्रश्‍न

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


Verify that y = cx + 2c2 is a solution of the differential equation 

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

Differential equation \[\frac{d^2 y}{d x^2} + y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 1\] Function y = sin x + cos x


Differential equation \[\frac{d^2 y}{d x^2} - y = 0, y \left( 0 \right) = 2, y' \left( 0 \right) = 0\] Function y = ex + e−x


x cos2 y  dx = y cos2 x dy


xy dy = (y − 1) (x + 1) dx


\[\frac{dy}{dx} = \frac{x\left( 2 \log x + 1 \right)}{\sin y + y \cos y}\]

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


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

Solve the differential equation \[\left( 1 + x^2 \right)\frac{dy}{dx} + \left( 1 + y^2 \right) = 0\], given that y = 1, when x = 0.


In a bank principal increases at the rate of r% per year. Find the value of r if ₹100 double itself in 10 years (loge 2 = 0.6931).


\[\frac{dy}{dx} + 1 = e^{x + y}\]

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

(x2 − y2) dx − 2xy dy = 0


Solve the following initial value problem:
\[x\frac{dy}{dx} + y = x \cos x + \sin x, y\left( \frac{\pi}{2} \right) = 1\]


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 to the curve satisfying x (x + 1) \[\frac{dy}{dx} - y\]  = x (x + 1) and passing through (1, 0).


If sin x is an integrating factor of the differential equation \[\frac{dy}{dx} + Py = Q\], then write the value of P.


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


Determine the order and degree of the following differential equations.

Solution D.E
y = aex + be−x `(d^2y)/dx^2= 1`

Determine the order and degree of the following differential equations.

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

Solve the following differential equation.

`(dθ)/dt  = − k (θ − θ_0)`


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.


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

Differential equation of the function c + 4yx = 0 is


For the differential equation, find the particular solution

`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0


Solve the following differential equation y2dx + (xy + x2) dy = 0


Choose the correct alternative:

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


Verify y = `a + b/x` is solution of `x(d^2y)/(dx^2) + 2 (dy)/(dx)` = 0

y = `a + b/x`

`(dy)/(dx) = square`

`(d^2y)/(dx^2) = square`

Consider `x(d^2y)/(dx^2) + 2(dy)/(dx)`

= `x square + 2 square`

= `square`

Hence y = `a + b/x` is solution of `square`


Integrating factor of the differential equation `"dy"/"dx" - y` = cos x is ex.


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


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