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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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A simple harmonic motion is given by the equation y=5(sin3t+3cos3t).you can avoid this part if you feel so. v= u + at. s =( u + v ) t /2. s = ut + at2/2. v2 = u2 + 2as.

We can also move denominator to the other side of the equation by changing it into numerator on the other side.

So lets review: RULE #1: you can add, subtract, multiply and divide by anything, as long as you do the same thing to both sides of the equals sign. RULE #2: to move or cancel a quantity or variable on one side of the equation, perform the opposite operation with it on both sides of the equation.

These relations are collectively known as the equation of motion. There are three equations of motion.

The three equations are, v = u + at. v = u + 2as. s = ut + at

In the same manner fourth equation of motion[S = vt at2] and fifth equation of motion [S = (u + v) t] is also derived from velocity-time graph.

The equations are as follows: v=u+at,s=(u+v2)t,v2=u2+2as,s=ut+12at2,s=vt12at2.

Rearranging equations For example, To rearrange the equation so that it is written as take each term and move to the other side of the equal sign using the opposite operation until you only have. e.g. Rearrange to make the subject of the equation. Take to the other side of the equal sign by adding to both sides.

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