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.
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 ……………