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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

Verify that y2 = 4ax is a solution of the differential equation y = x \[\frac{dy}{dx} + a\frac{dx}{dy}\]


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


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

Function y = ex + 1


\[\frac{dy}{dx} = x^2 + x - \frac{1}{x}, x \neq 0\]

(ey + 1) cos x dx + ey sin x dy = 0


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

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

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

Solve the differential equation \[x\frac{dy}{dx} + \cot y = 0\] given that \[y = \frac{\pi}{4}\], when \[x=\sqrt{2}\]


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).


\[\frac{dy}{dx} = \frac{\left( x - y \right) + 3}{2\left( x - y \right) + 5}\]

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

(x2 − y2) dx − 2xy dy = 0


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

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


Solve the following initial value problem:-

\[\frac{dy}{dx} + 2y \tan x = \sin x; y = 0\text{ when }x = \frac{\pi}{3}\]


Find the curve for which the intercept cut-off by a tangent on x-axis is equal to four times the ordinate of the point of contact.

 

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


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The price of six different commodities for years 2009 and year 2011 are as follows: 

Commodities A B C D E F

Price in 2009 (₹)

35 80 25 30 80 x
Price in 2011 (₹) 50 y 45 70 120 105

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Solve the following differential equation.

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


Solve the following differential equation.

`dy /dx +(x-2 y)/ (2x- y)= 0`


Solve the following differential equation.

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


Choose the correct alternative.

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

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Choose the correct alternative:

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


State whether the following statement is True or False:

The integrating factor of the differential equation `("d"y)/("d"x) - y` = x is e–x 


Solve the following differential equation `("d"y)/("d"x)` = x2y + y


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