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 .

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.