Solve the initial value problem. \frac{d^2y}{dx^2} = 4 \sec^2 x; y'(\frac {\pi}{4}) = 0; y(0) = 0...


Solve the initial value problem.

{eq}\frac{d^2y}{dx^2} = 4 \sec^2 x;~y'(\frac {\pi}{4}) = 0;~y(0) = 0 {/eq}

The solution is {eq}y = {/eq}

(Type an exact answer, using {eq}\pi {/eq} as needed.)

Initial Value Problem:

With the help of the indefinite integration, we can find the {eq}(m-1)^{th} {/eq} order derivative by integrating the {eq}m^{th} {/eq} order derivative. For example, we can obtain {eq}f'(x)+C {/eq} on integrating {eq}\displaystyle\int f''(x)\ \text dx. {/eq} The result will contain an arbitrary constant which can be easily eliminated by plugging the given initial conditions.

Answer and Explanation: 1

Become a member to unlock this answer!

View this answer

Given equation: {eq}\dfrac{d^2y}{dx^2} = 4 \sec^2 x\Rightarrow y''(x)=4\sec^2 x {/eq}

Now, we will integrate both sides using the rule...

See full answer below.

Learn more about this topic:

Initial Value in Calculus: Definition, Method & Example


Chapter 11 / Lesson 13

Learn to define the initial value problem and initial value formula. Learn how to solve initial value problems in calculus. See examples of initial value problems.

Related to this Question

Explore our homework questions and answers library