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joeduf
27.07.2019 •
Mathematics
What is the slope of the tangent line to the graph of a solution of y' = 6y + 5x that passes through (-1, 4) ans: in problems 6 and 7, verify the indicated function is an explicit solution of the given differential equation. 6. y' + y = sec x; y = x sin x + (cos x) incos x) ans: 7. x®y + xy + y = sec(in x); y = cos(in x) in(cos(in x)) + (in x) sin(in x) ans: 8. verify that the indicated expression is an implicit solution of the given differential equation. com +1 = (x 5)2 + yº = 1 ans: 9. y = c, ex + c, e* - 2x is a two parameter family of the second-order de y" - 2y' - 3y = 6x + 4. find a solution of the second order ivp consisting of the differential equation and the initial condition y(0) = 1, y'(0) = -3. ans:
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Ответ:
A. x = 1 , y = -2.
B. They will intersect at the point (1, -2).
Step-by-step explanation:
A.
y = 3x - 5
y = 6x - 8 We simply subtract the second equation from the first. This eliminates y:
0 = 3x - 6x - 5 - (-8)
0 = -3x - 5 + 8
3x = 3
x = 1
Now substitute for x in first equation:
y = 3(1) - 5
y = -2.
B. x = 1 and y = -2 are the values that satisfy both equations. So the liones will intersect at this point (1, -2).