Find solution to initial value problem: y'' +4y' +7y = 0; y(0) = 1, y'(0) = -2
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What you do is you rearrange and simplify both equations to have them in terms of y, and then graph them. If it asked for a solution, their point of intersection would be the solution.
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points =
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope =
slope =
We know slope =4
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7