Solving Initial Value Problems Using Integration | f'(x)=(x^2-1)/x^5, f(1/2)=3

In summary, the task is to solve the initial value problem: f'(x)=(x^2-1)/x^5 with the given initial condition f(1/2)=3. The integration process is correct, but the constant term needs to be added. After finding the value of C, it can be substituted to solve for the original function.
  • #1
howsockgothap
59
0

Homework Statement



Solve each of the following initial value problems: a) f'(x)=(x2-1)/x5 f(1/2)=3

Homework Equations





The Attempt at a Solution


I guess my problem with this is I'm not 100% sure what I'm being asked to do. I know I need to use integration to find the original function. Ok no prob I got -1/2x-2+1/4-4. So after that am I just supposed to plug in 3=the original function, substituting 1/2 for x? That doesn't seem right since I'm not getting 3... Am I doing the question incorrectly or have I done my integration wrong?
 
Last edited:
Physics news on Phys.org
  • #2
howsockgothap said:
Solve each of the following initial value problems: a) f'(x)=(x2-1)/x5

You're leaving out the whole problem. Did the question say f(1/2) = 3? Or f(3) = 1/2? As far as your integral goes, it looks fine to me if you mean [tex]\frac{-1}{2x^2}+\frac{1}{4x^4}[/tex]. However, don't forget to add a constant everytime you take an integral, so just put a +C at the end. After that, just plug in the x and f(x) values to solve for C.
 
  • #3
Ohhh so I'm solving for C. Thanks!
 

Related to Solving Initial Value Problems Using Integration | f'(x)=(x^2-1)/x^5, f(1/2)=3

1. What is an initial value problem?

An initial value problem is a type of differential equation that involves finding a function or equation that satisfies certain conditions at a specific point, known as the initial value. In this case, the initial value is f(1/2)=3.

2. How do you solve an initial value problem using integration?

To solve an initial value problem using integration, we first need to rewrite the given equation using the derivative notation, f'(x). Then, we integrate both sides of the equation and solve for the constant of integration using the given initial value.

3. What is the general process for solving initial value problems?

The general process for solving initial value problems involves rewriting the equation using the derivative notation, integrating both sides, and solving for the constant of integration using the given initial value. This process may vary depending on the type of differential equation and initial value given.

4. How do you determine the constant of integration in initial value problems?

The constant of integration is determined by using the given initial value. This value is substituted into the equation after integration, and then solved for the constant. In this case, the initial value of f(1/2)=3 is used to find the constant of integration.

5. Can initial value problems be solved using other methods besides integration?

Yes, initial value problems can also be solved using other methods such as separation of variables, substitution, and numerical methods. However, integration is a common and widely used method for solving initial value problems.

Similar threads

Find f(x,y) given partial derivative and initial condition
    • Calculus and Beyond Homework Help
Replies
6
Views
615
Solve the initial value problem
    • Calculus and Beyond Homework Help
Replies
1
Views
994
At what ##x## value is the tangent equally inclined to the given curve?
    • Calculus and Beyond Homework Help
Replies
5
Views
319
How should I calculate the stationary value of ## S[y] ##?
    • Calculus and Beyond Homework Help
Replies
2
Views
597
Two Solutions for y' = 5x^3(y-1)^1/5 with Initial Condition y(0)=1
    • Calculus and Beyond Homework Help
Replies
11
Views
1K
Verify Green's Theorem in the given problem
    • Calculus and Beyond Homework Help
Replies
10
Views
554
Centroid calculation using integrals
    • Calculus and Beyond Homework Help
Replies
9
Views
834
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
    • Calculus and Beyond Homework Help
Replies
7
Views
769
If f is undefined at x=a, can f' exist at x=a?
    • Calculus and Beyond Homework Help
Replies
9
Views
975
Find the constrained maxima and minima of ##f(x,y,z)=x+y^2+2z##
    • Calculus and Beyond Homework Help
Replies
2
Views
558

Hot Threads

Recent Insights

Back
Top