# 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).

Q1:

Find a particular solution for the following differential equation for which :

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Q2:

Find the solution for the following differential equation for :

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Q3:

Find the solution for the following differential equation for :

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Q4:

Find the solution for the following differential equation for :

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Q5:

Find the particular solution for the following separable differential equation: .

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Q6:

Find the solution for the following differential equation for :

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Q7:

Find the solution for the following differential equation for :

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Q8:

Find the solution for the following differential equation for :

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Q9:

For a circuit containing a capacitor and a resistor, the first-order differential equation that describes a discharging capacitor is If represents the charge within the capacitor at , find the general solution. is the capacitance of the capacitor. is the resistance of the resistor.

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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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Q13:

Find the solution for the following differential equation for :

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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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Q17:

Find the function, if , when and .

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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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