First Order Linear Differential Equations
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- เผยแพร่เมื่อ 19 ก.ย. 2024
- This calculus video tutorial explains provides a basic introduction into how to solve first order linear differential equations. First, you need to write the equation in standard form [y' + P(x)y = Q(x)] and then identify the functions P(x) and Q(x). Next, you need to determine the integrating factor I(x) using the formula I(x) = e^(integral of P(x)dx). Finally, you can use another formula to find the general solution of the first order linear differential equation y = 1/I(x) [Integral(I(x)Q(x)dx + C]. This video contains plenty of examples and practice problems on solving first order linear differential equations.
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00:00 -how to
01:13 -prob1
04:28 -prob2
10:24 -prob3
18:58 -prob4
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13:41 - prob 4
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In the last example, you can simply separate the equation (x² - y)/x into two terms: x - y/x. Goes the same answer, sir.
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Professor Organic Chemistry Tutor, thank you for another fantastic video/lecture on First Order Linear Differential Equations. Introductory Differential Equations books use a different method to solve First Order Linear Differential Equations. Many Introductory Differential Equations books after finding the Integrating Factor, use it to multiply the standard form equation and then solve for y. This is an error free video/lecture on TH-cam TV with the Organic Chemistry Tutor.
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for the last problem, you can simply spit apart the fraction and make it x^/x and -y/x. then I added y/x to both sides and got dy/dx +y/x = x^2/x. This leaves you with a P(X)= 1/x and a Q(x)= x as well.
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For the last example there's a much quicker way to get it into standard form. Re-write (x^2-Y)/X as X^2/X - Y/X and the just add the Y/X term to the left side.
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