A third-order homogeneous linear equation and three linearly independent solutions are given below. Find a particular solution satisfying the given initial conditions. x°yl8) - 3xy" + 6xy' – 6y = 0; y(1) = 8, y'(1) = 12, y'"(1) = 30; Y1 = x, Y2 =x², y3 =x The particular solution is y(x) =-

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: