Solution of the differential equation of the type `("d"x)/("d"y) + "p"_1x = "Q"_1` is given by x.I.F. = `("I"."F") xx "Q"_1"d"y`.

Solution of the differential equation of the type ddpQdxdy+p1x=Q1 is given by x.I.F. = IFQd(I.F)×Q1dy. - Mathematics

Question

Solution of the differential equation of the type $\frac{d x}{d y} + p_{1} x = Q_{1}$ is given by x.I.F. = $(I . F) \times Q_{1} d y$ .

Options

True
False

MCQ

True or False

Solution

This statement is True.

Explanation:

Since particular solution of a differential equation has no arbitrary constant.

shaalaa.com

Solutions of Linear Differential Equation

Is there an error in this question or solution?

Q 77.(ii)Q 77.(i)Q 77.(iii)

Chapter 9: Differential Equations - Exercise [Page 202]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12

Chapter 9 Differential Equations
Exercise | Q 77.(ii) | Page 202

Video TutorialsVIEW ALL [2]

view
Video Tutorials For All Subjects
Solutions of Linear Differential Equation

video tutorial00:19:38
Solutions of Linear Differential Equation

video tutorial00:33:51

RELATED QUESTIONS

Solve the following differential equation: $(x^{2} - 1) \frac{d y}{d x} + 2 x y = \frac{2}{x^{2} - 1}$

Solve the differential equation $(1 + x 2) \frac{d y}{d x} + y = e^{\tan^{- 1}} x .$

Solve $\sin x \frac{d y}{d x} - y = \sin x . \tan \frac{x}{2}$

4 \frac{d y}{d x} + 8 y = 5 e^{- 3 x}

\frac{d y}{d x} + 2 y = 4 x

x \frac{d y}{d x} + y = x e^{x}

\frac{d y}{d x} + \frac{4 x}{x^{2} + 1} y + \frac{1}{{(x^{2} + 1)}^{2}} = 0

x \frac{d y}{d x} - y = (x - 1) e^{x}

\frac{d y}{d x} + y = \sin x

$\frac{d y}{d x}$ = y tan x − 2 sin x

$\frac{d y}{d x}$ + y cot x = x² cot x + 2x

Find the equation of the curve passing through the point (0, 2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.

A wet porous substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.

Solve the differential equation: (1 + x²) dy + 2xy dx = cot x dx

Solve the differential equation : $x \frac{d y}{d x} + y - x + xy \cot x = 0; x \neq 0 .$

If e^x + e^y = e^x+y, then $\frac{dy}{dx}$ is:

Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2^nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3^rd week can be estimated using the solution to the differential equation $\frac{dy}{dx} = k (50 - y)$ where x denotes the number of weeks and y the number of children who have been given the drops.

The solution of the differential equation $\frac{dy}{dx} = k (50 - y)$ is given by ______.

Which of the following solutions may be used to find the number of children who have been given the polio drops?

If α, β are different values of x satisfying the equation a cos x + b sinα x = c, where a, b and c are constants, then $\tan (\frac{α + β}{2})$ is

The solution of the differential equation $\frac{d y}{d x} = 1 + x + y + x y$ when y = 0 at x = – 1 is

$\int \cos (\log x) d x = F (x) + C$ where C is arbitrary constant. Here F(x) =

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.

Solve the following differential equation: (y – sin²x)dx + tanx dy = 0

Let y = y(x) be the solution of the differential equation $\frac{d y}{d x} + \frac{\sqrt{2} y}{2 \cos^{4} x - \cos 2 x} = x e^{\tan^{- 1} (\sqrt{2} \cos t 2 x)}, 0 < x < \frac{π}{2}$ with $y (\frac{π}{4}) = \frac{π^{2}}{32}$ . If $y (\frac{π}{3}) = \frac{π^{2}}{18} e^{- \tan^{- 1} (α)}$ , then the value of 3α² is equal to ______.

The population P = P(t) at time 't' of a certain species follows the differential equation $\frac{dp}{dt}$ = 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is ______.

Let y = y(x) be the solution of the differential equation, $\frac{2 + \sin x d y}{y + 1} \frac{d y}{d x}$ = –cosx. If y > 0, y(0) = 1. If y(π) = a, and $\frac{d y}{d x}$ at x = π is b, then the ordered pair (a, b) is equal to ______.

Solution of the differential equation of the type ddpQdxdy+p1x=Q1 is given by x.I.F. = IFQd(I.F)×Q1dy. - Mathematics

Advertisements

Advertisements

Question

Options

Solution

APPEARS IN

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Select a course

Solution of the differential equation of the type ddpQdxdy+p1x=Q1 is given by x.I.F. = IFQd(I.F)×Q1dy. - Mathematics

Advertisements

Advertisements

Question

Options

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Select a course

Solution