Calculus matematik 4 matematik 5

Differential equations of the second order

Second order differential equations of the homogen type

y” (x)+ a y'(x) + by(x) = 0

are possible to solve with the aid of the characteristic equation

r2 + a r +b =0

If this have the roots r1 and r2  

the solution is given by

y(x) = Cer1x + Der2 x  

If the equation is inhomogenous and the right side is a polynom assume a solution a polynomial of the same degree

If the right side is a trigonometric function assume a as a solution a combination of trigonometric functions.

Ex. Solve the equation y” -3y – 4y = 0

Solve the characteristic equation: r2-3r-4 = 0
r=4 och r = -1.

The general solution is y = Ce-4x + Dex
Where C and D are arbetare constants.

Av mattelararen

Licentiate of Philosophy in atomic Physics
Master of Science in Physics

2 svar på ”Differential equations of the second order”


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