# Worksheet: Indefinite Integrals and Initial Value Problems

In this worksheet, we will practice using integration to find particular solutions to initial value problems involving differential equations of the form y' = f(x).

**Q10: **

Find the solution of the differential equation that satisfies the initial condition .

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**Q11: **

Find the solution of the differential equation , where , that satisfies the initial condition .

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**Q12: **

Solve the differential equation for given that .

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**Q14: **

You are told that . If and , which of the following is equal to ?

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**Q15: **

Find the function whose first derivative is given the value of the function equals when equals .

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**Q16: **

Suppose that and when . Find in terms of .

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**Q18: **

Determine the function satisfying , , and .

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**Q19: **

Determine the function if , , , and .

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**Q20: **

Suppose that and when . Find in terms of .

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**Q21: **

Determine the function if , , and .

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**Q22: **

Find the function on which satisfies , , and .

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**Q23: **

Determine the function satisfying , , and .

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**Q24: **

The function satisfies the relation where and is a constant. Find given and .

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**Q25: **

Given that , and when , find the relation between and .

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