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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
Multiply both sides of the equation by dx, we have
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
Substitute the above equation to the original equation, we have
where
