The special solution of the differential equation y '= e ^ x + y satisfying the condition y (0) = 0 is

freedombless ,
This problem is very simple. Y '= e ^ x + y becomes y' - y = e ^ X. if both ends of the equation are multiplied by e ^ (- x), it becomes e ^ (- x) y '- Ye ^ (- x) = 1, and the left end of the equation is approximated to [y * e ^ (- x)]' and both sides are integrated at the same time to get Ye ^ (- x) = x + C. the process of finding the general solution is called integral factor method
The above formula is the general solution. When the initial condition y (0) = 0, x = 0, y = 0, C = 0 is obtained by substituting the above formula, so the special solution of the original differential equation is y = Xe ^ X

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