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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