Separation of Variables, 36

Category: Differential Equations

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Find the general solution for

Solution:

Consider the given equation above  

Express y' as dy/dx as follows

By separation of variables, transpose x² dx to the right side of the equation and e^y to the left side of the equation, we have

Integrate on both sides of the equation, we have  

Therefore, the general solution is

where G = - C.