Find the particular solution of the differential equation that satisfies the initial condition(s). f ''(x) = x−3/2, f '(4) = 1, f(0) = 0

Hence, the particular solution of the differential equation is .

Step-by-step explanation:

This differential equation has separable variable and can be solved by integration. First derivative is now obtained:

, where C is the integration constant.

The integration constant can be found by using the initial condition for the first derivative ():

The first derivative is , and the particular solution is found by integrating one more time and using the initial condition ():

Hence, the particular solution of the differential equation is .

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step-by-step explanation: