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in this video were going to talk about how to solve first order linear differential equations now the first thing you need to do is you need to write it in standard form and that is y prime plus p of x times y which is equal to q of x now once you have it in standard form you need to identify the functions p of x and q of x now the next thing you need to do is determine the integrating factor which is e raised to the integral of p x dx now once you have the integrating factor you can now write the general solution to the differential equation so its going to be 1 divided by the integrated factor times the integral of i of x times q of x dx and then plus some constant of integration now once you integrate this portion to get the integrating factor and dont add the constant of integration you should only add it at the very end in this step so keep that in mind now lets work on some problems so lets say if we have this differential equation y prime plus 2y is equal to 2e to the x so

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Equations with one solution You can tell that an equation has one solution if you solve the equation and get a variable equal to a number.

There are three methods used to solve systems of equations: graphing, substitution, and elimination.

A differential equation of the form `dy/dx+Py=Q` is said to be a linear differential equation. Integrating factor of this differential equation is `e^(intPdx)` and its solution is given by `y.e^(int Pdx)=int (Qe^(int Pdx))dx+c`.

It is commonly used to solve ordinary differential equations, but is also used within multivariable calculus when multiplying through by an integrating factor allows an inexact differential to be made into an exact differential (which can then be integrated to give a scalar field).

0:00 0:39 Satisfying Equations - College Algebra - YouTube YouTube Start of suggested clip End of suggested clip One lets say we can figure out its coordinates substitute them in to x and y respectively. And thenMoreOne lets say we can figure out its coordinates substitute them in to x and y respectively. And then find the two sides of the equation are equal to one another in principle.

0:18 6:53 How to Solve: Does the function satisfy the differential equation? YouTube Start of suggested clip End of suggested clip And you can do this to see if you got the right answer. So the three steps were going to go throughMoreAnd you can do this to see if you got the right answer. So the three steps were going to go through in every process is first youre going to differentiate the Y equation. Thats given to get a y

A value (or values) that solve an equation. Example: 2x + 1 = 9. x=4 solves the equation (we get 8 + 1 = 9, which is true), so x=4 satisfies the equation. See: Equation. Introduction to Algebra.

What are The Steps in Solving Equations? Remove the brackets, if any in the given equation. Apply the distributive property. Add the same number to both the sides. Subtract the same number from both the sides. Multiply the same number on both the sides. Divide by the same number on both sides.

A solution is a function y=f(x) that satisfies the differential equation when f and its derivatives are substituted into the equation.

The solution to a system of linear equations is the point at which the lines representing the linear equations intersect.

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