Solving y'=y-sin(2x): Integral of -sin(2x)e^x Stuck, Help!

  • Thread starter koolrizi
  • Start date
In summary, the integrating factor for the given differential equation is e^x and the integral of -sin(2x)e^x can be solved by using integration by parts. However, it is possible to solve for the expression directly, resulting in the answer 1/5(sin(2x)+2cos(2x)). Just be careful with the details, such as using the correct integrating factor and including the boundaries of the LHS of the equation.
  • #1
koolrizi
21
0
I found the integrating factor to be e^x for DE y'=y-sin(2x)
Now i am stuck at integral of -sin(2x)e^x
Can you help me with it? I tried using integration by parts and i get to following
integral(sin(2x)(e^x)=sin(2x)e^x-2cos(2x)e^x-4*integral(sin(2x)(e^x)

I am stuck. Help! Thanks
 
Physics news on Phys.org
  • #2
Notice that you have the expression "integral(sin(2x)(e^x))" on both sides of your equation. You can therefore solve for it directly, and be done.
 
  • #3
directly? I think i am not seeing something
 
  • #4
The answer to this DE is 1/5(sin(2x)+2cos(2x) and i am not seeing how to get to this from what i have
 
  • #5
OH ok i got it...wasnt seeing that lol...THanks
 
  • #6
also careful with your results. looks like you missed a couple small details. your integrating factor is actually $e^{-x}$ and you should have the boundaries of the LHS of your equation(unless they're supposed to be =0)
 

FAQ: Solving y'=y-sin(2x): Integral of -sin(2x)e^x Stuck, Help!

What is the first step in solving y'=y-sin(2x)?

The first step is to separate the variables by moving all terms involving y to one side of the equation and all terms not involving y to the other side. This will give you the equation y' - y = -sin(2x).

How do I solve for y?

To solve for y, you will need to use an integrating factor. This is the function e^x, which is multiplied by both sides of the equation. This will simplify the left side of the equation to (e^x)y' - (e^x)y = -(sin(2x)e^x).

What is the integrating factor?

The integrating factor is the function e^x, which is multiplied by both sides of the equation to simplify the left side of the equation.

How do I solve the integral of -sin(2x)e^x?

To solve this integral, you will need to use integration by parts. The formula for integration by parts is ∫u dv = uv - ∫v du. In this case, let u = e^x and dv = -sin(2x). You can then solve for v and du, plug them into the formula, and integrate to find the solution.

What is the final solution for y?

After solving the integral of -sin(2x)e^x, you will get an expression for y in terms of x. The final solution will be y = (c + 1/2)e^x - 1/4sin(2x)e^x, where c is the constant of integration.

Similar threads

Differentiate the given integral
Replies
15
Views
1K
Arc length of vector function - the integral seems impossible
Replies
2
Views
1K
##\lim_{x \to0} \left(\dfrac{1}{\sin^2 x}-\dfrac{1}{x^2}\right)##
Replies
5
Views
207
First Order Diffy Q Problem with Bernoulli/Integrating Factors
Replies
4
Views
1K
How Do You Correctly Apply Integration by Parts to ∫-e^(2x)*sin(e^x) dx?
Replies
9
Views
1K
Solve the given first order differential equation
Replies
8
Views
1K
Solve the given problem involving integration
Replies
6
Views
605
Solve p = P(2X <= Y^2) using double integral
Replies
4
Views
1K
Write |exp(2z+i)| in terms of x and y
Replies
6
Views
2K
For what range of x is (e^x-1)/2x=0.5 correct to 15 decimal digits?
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top