# Worksheet: Initial Value Problems

In this worksheet, we will practice finding a specific solution to a separable differential equation given an initial value.

Q1:

Find the equation of the curve that passes through the point given that the gradient of the tangent at any point is .

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Q2:

Find the equation of the curve that passes through the point given .

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Q3:

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

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Q4:

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

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Q5:

Suppose that and when . Find in terms of .

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Q6:

A relation is implicitly differentiated to obtain . Find the relation given that when , .

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Q7:

Find the equation of the curve that passes through the point given that the gradient of the tangent at any point is equal to 2 times the square of the coordinate.

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Q8:

Suppose that and when . Find in terms of .

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Q9:

Find the solution of the differential equation given that .

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Q10:

Find the solution for the following differential equation for :

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Q11:

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

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Q12:

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

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Q13:

Find the solution for the following differential equation for :

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Q14:

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

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Q15:

Find the solution of the differential equation that passes through the point .

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