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Find the particular solution that satisfies the initial condition.

0 votes

Find the particular solution that satisfies the initial condition.

Differential equation                                         Initial condition

asked Feb 11, 2015 in CALCULUS by anonymous

1 Answer

0 votes

Step 1:

The differential equation is image and the initial condition is image.

Consider image.

Re-write the equation.

image

Multiply and divide each side by 2.

image

Integrate on each side.

image

Step 2:

image

The solution of the differential equation is image.

The initial condition is image.

Substitute image and image in the solution of the differential equation.

image

Substitute image in the solution of the differential equation.

image

Take exponents of each side.

image

Properties of natural logarithms: image.

image

The solution of the differential equation is image.

Solution:

The solution of the differential equation is image.

answered Feb 16, 2015 by Lucy Mentor

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