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Chapter 2: Q. 5TF (page 223)

Show that yx=4e3xis a solution of the differential

equation dydx=3y

Short Answer

Expert verified

Hence proved

Step by step solution

01

Step 1. Given information

Givenyx=4e3x

02

Step 2. Solve the value

yx=4e3xdyxdx=d4e3xdx=4e3x3=3yxdyxdx=3yx

Hence proved

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Most popular questions from this chapter

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=3x+1x2+1

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that is perpendicular to the tangent line to f(x)=x4+1at x=2 and also passes through the point(-1,8)

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=(x4-8)(1-3x5);f(0)=2

Use the definition of the derivative to find f'for each function fin Exercises39-54

f(x)=21-x

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line tangent to the graph of y=4x+3 at the point(-2,-5)
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