We want to solve the inhomogeneous second-order linear differential equation d²y dx² First we find the general solution to the corresponding homogeneous equation +3 Finally, suppose that y = d² y dx² dy (x) - 10 y = - sin(5 x) dx +3 (d) -10, - 10 y = 0 C y = Next we find the particular solution to the inhomogeneous equation (*). To do this, first we choose a trial solution of the form y = C sin(5 x) + D cos(5 x). Substitute this into the left-hand side of (*), and compare coefficients with the right-hand side to find the correct values for the constants. Write down this particular solution: y = Now write down the full general solution to the inhomogeneous equation (*): y = 2439 3619 and = = when x = 0. Find the specific solution to the inhomogeneous equation (*) that satisfies these initial conditions: y = 290 290 C
We want to solve the inhomogeneous second-order linear differential equation d²y dx² First we find the general solution to the corresponding homogeneous equation +3 Finally, suppose that y = d² y dx² dy (x) - 10 y = - sin(5 x) dx +3 (d) -10, - 10 y = 0 C y = Next we find the particular solution to the inhomogeneous equation (*). To do this, first we choose a trial solution of the form y = C sin(5 x) + D cos(5 x). Substitute this into the left-hand side of (*), and compare coefficients with the right-hand side to find the correct values for the constants. Write down this particular solution: y = Now write down the full general solution to the inhomogeneous equation (*): y = 2439 3619 and = = when x = 0. Find the specific solution to the inhomogeneous equation (*) that satisfies these initial conditions: y = 290 290 C
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:We want to solve the inhomogeneous second-order linear differential equation
d² y
dx²
First we find the general solution to the corresponding homogeneous equation
Finally, suppose that y =
2439
290
+3
3619
290
d² y
dx²
dy
(dx) - 10 y = - sin(5 x)
y =
Next we find the particular solution to the inhomogeneous equation (*). To do this, first we choose a trial solution of the form y = C sin(5 x) + D cos(5 x). Substitute this into the
left-hand side of (*), and compare coefficients with the right-hand side to find the correct values for the constants.
Write down this particular solution: y =
Now write down the full general solution to the inhomogeneous equation (*): y =
dy
and =
dx
+3
dy) - 10 y = 0
dx
when x = 0. Find the specific solution to the inhomogeneous equation (*) that satisfies these initial conditions: y =
(*)
(†)
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