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Find the general solution for
Solution:
Consider the given equation above
The given equation is a 2nd Order Differential Equation because the second derivative of y with respect to x is involved. We can rewrite given equation as follows
Multiply both sides of the equation by dx, we have
Integrate on both sides of the equation, we have
Since the degree of a variable for both numerator and denominator are the same, then we have to do the division of a polynomial with another polynomial. After the division, the right side of the equation becomes
Multiply both sides of the equation by dx, we have
Integrate on both sides of the equation, we have
Consider
If
then
If
then
Hence, by integration by parts
Since the degree of a variable for both numerator and denominator are the same, then we have to do the division of a polynomial with another polynomial. After the division, the right side of the equation becomes
Substitute the above equation to the original equation, we have
