particular solution for differential equations

[james_j966]

hi

i need help solving these two differential equations as particular solutions;

12 (d^2 y)/(dt^2 )-3y=0 given that when t=0, y=3 and dy/dx= 1/2

and

(d^2 y)/(dx^2 )+2 dy/dx+2y=10e^x given that when x = 0, y = 0 and dy/dx=1

thanks

 

[Deleted member 4993]

hi

i need help solving these two differential equations as particular solutions;

12 (d^2 y)/(dt^2 )-3y=0 given that when t=0, y=3 and dy/dx= 1/2

and

(d^2 y)/(dx^2 )+2 dy/dx+2y=10e^x given that when x = 0, y = 0 and dy/dx=1

thanks

You have serious problems with your post (problem #1).

1. You have a DE with 't' as your independent variable - yet you have one boundary condition with 'x' as independent variable (dy/dx = 1/2).
   
   
2. You have a homogeneous DE - there is NO particular solution. You will have a solution of the form:
   
   y = A * f₁(t) + B * f₂(t) ...... and you would solve for A and B using the initial conditions.

For the problem # 2

Please make separate threads for different problems.​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[Steven G]

I just want to inform you that this forum is not a homework service forum. We do not solve problems for student. As the url would suggest we are a math help forum. Getting help with you math homework and having someone do the work for you are not the same. On this forum we expect that you solve your own problems with helpful hints from us.

So please read our guidelines, follow them and then post back.

 

[james_j966]

firstly i do not appreciated the tone in which you have sent your message secondly i have already worked out the answer for the equation i simply wanted to validate my answer and methodology i used to get it.
(-3y(x)=0,t=0,y(x)=3,y(x)=1/2)

 

[HallsofIvy]

So in addition to helping you people have to do it with "right tone"? Gosh, how much are you paying them?

 

[james_j966]

common courtesy to not be rude but by the looks of it theirs more then one rude person on here

 

[MarkFL]

common courtesy to not be rude but by the looks of it theirs more then one rude person on here

We don't actually consider it to be rude when pointing out errors in the statement of a problem, nor in asking that our guidelines for posting be followed. No one meant any malice, it's just that we expect to see exactly where you are stuck so we can better help.

Let's look at the first IVP you posted and walk through it step by step:

[MATH]12\frac{d^2y}{dt^2}-3y=0[/MATH] where [MATH]y(0)=3,\,y'(0)=\frac{1}{2}[/MATH]
Note: I am assuming the first derivative is for \(t=0\).

I would divide the ODE by 12 to get:

[MATH]\frac{d^2y}{dt^2}-\frac{1}{4}y=0[/MATH]
Now, we see we have a second order linear homogeneous ODE associated with our IVP. What are the characteristic roots?