# 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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**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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**Q14: **

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

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