Find the general solution for the differential equation \displaystyle{\left.{d}{y}\right.}+{9}{x}\ {\left.{d}{x}\right.}={0}dy+9
1 answer:
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Answer:
(x, y) = (2, -3/4)
Step-by-step explanation:
The point of the "elimination" technique is to combine the equations in a way that eliminates one of the variables. Sometimes this involves multiplying one or both of the equations by constants before you add those results together. In any event, the first step is to look at the coefficients of the variable terms to see if there is a simple combination of them that will result in zero.
The y terms have coefficients that are opposites of each other (4, -4), so you can simply add the two equations to eliminate y as a variable.
(2x +4y) +(x -4y) = (1) +(5)
3x = 6 . . . . . simplify
x = 2 . . . . . . divide by 3
Now, you find y by substituting this value into one of the equations. I would choose the equation with the positive y-coefficient:
2(2) +4y = 1
4y = -3 . . . . . . subtract 4
y = -3/4
Then the solution is ...
(x, y) = (2, -3/4)
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A graphing calculator confirms this solution.
