Calculus 1 : How to find solutions to differential equations

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #1311 : Functions

Find of the following equation:

Possible Answers:

Correct answer:

Explanation:

First take the derivative and then solve when x=2.

To find the derivative use the power rule which states when,

 the derivative is .

Therefore the derivative of our function is:

Example Question #261 : Equations

Find  for the following equation:

Possible Answers:

Undefined

Correct answer:

Explanation:

To find the derivative of this function we will need to use the product rule which states to multiply the first function by the derivative of the second function and add that to the product of the second function and the derivative of the first function. In other words,

To do this we will let,

 and 

 and 

Now we can find the derivative by plugging in these equations as follows.

Now plug in x=1 and solve.

Example Question #261 : Equations

Find the solution to the following equation at

Possible Answers:

Undefined

Correct answer:

Explanation:

To solve, we must first find the derivative and then solve when x=-2.

To find the derivative of the function we will use the Power Rule:

Therefore,

 

Now to solve for -2 we plug it into our x value.

 

Example Question #11 : How To Find Solutions To Differential Equations

Find for the following equation:

Possible Answers:

Correct answer:

Explanation:

First, find the derivative. Then, evaluate at x=3.

For this function we will use the Power Rule to find the derivative.

Also remember that the derivative of  is .

Therefore we get,

Example Question #262 : Equations

Find the particular solution given 

Possible Answers:

Correct answer:

Explanation:

The first thing we must do is rewrite the equation:

We can then find the integrals:

  The integrals are as follows:

We're left with:

We then plug in the initial condition and solve for 

The particular solution is then:

Example Question #1321 : Functions

Find the particular solution given 

Possible Answers:

Correct answer:

Explanation:

The first thing we must do is rewrite the equation:

We can then find the integrals:

  The integrals are as follows:

We're left with:

We then plug in the initial condition and solve for 

The particular solution is then:

Example Question #11 : Solutions To Differential Equations

Find the particular solution given .

Possible Answers:

Correct answer:

Explanation:

Remember: 

 

The first thing we must do is rewrite the equation:

We can then find the integrals:

The integrals are as follows:

We're left with:

We then plug in the initial condition and solve for 

The particular solution is then:

Example Question #11 : How To Find Solutions To Differential Equations

Find the particular solution given 

Possible Answers:

Correct answer:

Explanation:

The first thing we must do is rewrite the equation:

We can then find the integrals:

The integrals are as follows:

We're left with

We plug in the initial condition and solve for 

The particular solution is then:

Example Question #12 : How To Find Solutions To Differential Equations

Find the particular solution given 

Possible Answers:

Correct answer:

Explanation:

The first thing we must do is rewrite the equation:

We can then find the integrals:

The integrals are as follows:

 

We're left with

Plugging in the initial conditions and solving for c gives us:

The particular solution is then,

Example Question #1321 : Functions

Differentiate the polynomial.

Possible Answers:

Correct answer:

Explanation:

Using the power rule, we can differentiate our first term reducing the power by one and multiplying our term by the original power. , will thus become . The second term , will thus become . The last term is a constant value, so according to the power rule this term will become .

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