## How do you find the general solution?

General Solutions of a Trig EquationSolve sin(x) = y for x.Case 1: -1≤y≤ 1, that is, the value of y is between -1 and 1, so there is a solution.Case 2: -1 > y or y > 1 , that is, the value of y is too large or too small for a solution to be possible.Solve cos(x) = y for x.Case 1: -1≤y≤ 1.Solve tan(x) = y for x.

## How do you find the general and singular solution of a differential equation?

Another way to find a singular solution as the envelope of the family of integral curves is based on using C-discriminant. Let Φ(x,y,C) be the general solution of a differential equation F(x,y,y′)=0. Graphically the equation Φ(x,y,C)=0 corresponds to the family of integral curves in the xy-plane.

## What is the general solution of tan?

Hence, the general solution of tan θ = tan ∝ is θ = nπ + ∝, where n ∈ Z (i.e., n = 0, ± 1, ± 2, ± 3,…….) Note: The equation cot θ = cot ∝ is equivalent to tan θ = tan ∝ (since, cot θ = 1/tan θ and cot ∝ = 1/tan ∝). Thus, cot θ = cot ∝ and tan θ = tan ∝ have the same general solution.

## What does General solution mean?

1 : a solution of an ordinary differential equation of order n that involves exactly n essential arbitrary constants. — called also complete solution, general integral. 2 : a solution of a partial differential equation that involves arbitrary functions.

## What is linear equation in differential equation?

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form. where , , and are arbitrary differentiable functions that do not need to be linear, and.

## How do you solve first order differential equations?

Here is a step-by-step method for solving them:Substitute y = uv, and. Factor the parts involving v.Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)Solve using separation of variables to find u.Substitute u back into the equation we got at step 2.

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## What is singular solution of differential equation?

Singular solution, in mathematics, solution of a differential equation that cannot be obtained from the general solution gotten by the usual method of solving the differential equation. In the example given, y has its minimum value for each x when c = -x, giving the singular solution as indicated.

## What is clairaut’s equation of differential equation?

Clairaut’s equation, in mathematics, a differential equation of the form y = x (dy/dx) + f(dy/dx) where f(dy/dx) is a function of dy/dx only. The equation is named for the 18th-century French mathematician and physicist Alexis-Claude Clairaut, who devised it.

## What is particular solution?

: the solution of a differential equation obtained by assigning particular values to the arbitrary constants in the general solution.

## What is the formula of tan theta?

(Math | Trig | Identities)

sin(theta) = a / c csc(theta) = 1 / sin(theta) = c / a
cos(theta) = b / c sec(theta) = 1 / cos(theta) = c / b
tan(theta) = sin(theta) / cos(theta) = a / b cot(theta) = 1/ tan(theta) = b / a

## What is the general solution of Sinx 1?

Hence, the general solution of sin θ = 1 is θ = (4n + 1)π2, n ∈ Z. Therefore, either, 2 sin x + 3 = 0 ⇒ sin x = – 32, Which is impossible since the numerical value of sin x cannot be greater than 1. We know that the general solution of sin θ = 1 is θ = (4n + 1)π2, n ∈ Z. Therefore, x = (4n + 1)π2 ……………

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#### Equation of a trend line

How do you calculate a trend line? Lesson SummaryStep 1: Complete each column of the table.Step 2: Calculate the slope (m) of your trend line by dividing the total for Column 3 by the total for Column 4.Step 3: Calculate the y-intercept (b) of your trend line using the average of the slope from Step […]

#### What is the value of x in the equation

How do you find the value of x? In algebra, it is easy to find the third value when two values are given. Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and […]