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Saturday, November 10, 2012

Variable Separation - Arbitrary Constant

Category: Differential Equation, Integral Calculus

"Published in Newark, California, USA"

Find the particular solution for the equation:


when x = 0, y = 0.

Solution:

If you examine the given equation, it is a differential equation because of the presence of y'. The above equation can be written as





You notice that the exponent of e has two terms. The above equation can be written as


Next, arrange the above equation by separation of variables




Consider the left side of the equation. If u = -y, then du = -dy.

Consider the right side of the equation. If u = -x2, then du = - 2x dx.



Integrate both sides of the equation, we have




To solve for the value of C, substitute x = 0 and y = 0 to the above equation






Therefore, the particular solution is