# Worksheet: Initial Value Problems of Differential Equations

Q1:

Find the solution for the following differential equation for :

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Q2:

Suppose that and when . Find in terms of .

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Q3:

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

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Q4:

Solve the differential equation for given that .

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Q5:

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

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Q6:

Find the solution for the following differential equation for :

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Q7:

Solve the differential equation for given that .

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Q8:

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

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Q9:

Find the solution for the following differential equation for :

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Q10:

Find the solution for the following differential equation for :

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Q11:

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

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Q12:

Solve the differential equation for given that .

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Q13:

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

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Q14:

Find the solution for the following differential equation for :

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Q15:

Find the solution for the following differential equation for :

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Q16:

The gradient of the tangent to a curve is . Find the equation of the curve given that the curve passes through the point .

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Q17:

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

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Q18:

Find the solution for the following differential equation for :

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Q19:

The gradient of the tangent of a curve is and the curve passes through the point . Find the equation of the normal to the curve at the point where the -coordinate is .

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Q20:

Find the solution for the following differential equation for :

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Q21:

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

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Q22:

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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