हिंदी

Integrating factor of the differential equation dydxdydx-y = cos x is ex.

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is False.

Explanation:

Because I.F = `"e"^(int -1 "d"x)`

= e–x.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 9: Differential Equations - Solved Examples [पृष्ठ १९१]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 9 Differential Equations
Solved Examples | Q 23. (vi) | पृष्ठ १९१

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Solve the equation for x: `sin^(-1)  5/x + sin^(-1)  12/x = π/2, x ≠ 0`


\[x^2 \left( \frac{d^2 y}{d x^2} \right)^3 + y \left( \frac{dy}{dx} \right)^4 + y^4 = 0\]

Verify that y = 4 sin 3x is a solution of the differential equation \[\frac{d^2 y}{d x^2} + 9y = 0\]


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 Ax2 + By2 = 1 is a solution of the differential equation x \[\left\{ y\frac{d^2 y}{d x^2} + \left( \frac{dy}{dx} \right)^2 \right\} = y\frac{dy}{dx}\]

 


Show that the differential equation of which \[y = 2\left( x^2 - 1 \right) + c e^{- x^2}\]  is a solution is \[\frac{dy}{dx} + 2xy = 4 x^3\]


Differential equation \[\frac{d^2 y}{d x^2} - 3\frac{dy}{dx} + 2y = 0, y \left( 0 \right) = 1, y' \left( 0 \right) = 3\] Function y = ex + e2x


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

\[\frac{dy}{dx} = x \log x\]

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

\[x\frac{dy}{dx} + \cot y = 0\]

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

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

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


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

\[\frac{dy}{dx} = \left( \cos^2 x - \sin^2 x \right) \cos^2 y\]

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

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


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

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

Find the equation of the curve which passes through the point (2, 2) and satisfies the differential equation
\[y - x\frac{dy}{dx} = y^2 + \frac{dy}{dx}\]


The slope of the tangent at each point of a curve is equal to the sum of the coordinates of the point. Find the curve that passes through the origin.


The solution of the differential equation \[\frac{dy}{dx} - \frac{y\left( x + 1 \right)}{x} = 0\] is given by


The differential equation of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = C\] is


Which of the following is the integrating factor of (x log x) \[\frac{dy}{dx} + y\] = 2 log x?


The integrating factor of the differential equation \[\left( 1 - y^2 \right)\frac{dx}{dy} + yx = ay\left( - 1 < y < 1 \right)\] is ______.


y2 dx + (x2 − xy + y2) dy = 0


In the following verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:-

y = ex + 1            y'' − y' = 0


The solution of `dy/ dx` = 1 is ______.


Choose the correct alternative.

The solution of `x dy/dx = y` log y is


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

Bacterial increases at the rate proportional to the number present. If original number M doubles in 3 hours, then number of bacteria will be 4M in


Solve the differential equation (x2 – yx2)dy + (y2 + xy2)dx = 0


Solve: `("d"y)/("d"x) + 2/xy` = x2 


Solve the following differential equation

`yx ("d"y)/("d"x)` = x2 + 2y2 


Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0


Solve: `("d"y)/("d"x) = cos(x + y) + sin(x + y)`. [Hint: Substitute x + y = z]


lf the straight lines `ax + by + p` = 0 and `x cos alpha + y sin alpha = p` are inclined at an angle π/4 and concurrent with the straight line `x sin alpha - y cos alpha` = 0, then the value of `a^2 + b^2` is


`d/(dx)(tan^-1  (sqrt(1 + x^2) - 1)/x)` is equal to:


The differential equation (1 + y2)x dx – (1 + x2)y dy = 0 represents a family of:


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×