How Do You Solve an RLC Differential Equation with Given Starting Conditions?

[Bassalisk]

Homework Statement

Solve the differential equation(for voltage u_c(t) on the end of the capacitor in some electric circuit)
[PLAIN]http://pokit.etf.ba/get/402e740f4c35317784c20c0acd656de5.jpg
for independent starting conditions
[PLAIN]http://pokit.etf.ba/get/?f840b445d268567428ada50ed466c4f6.jpg
and dependent starting conditions
[PLAIN]http://pokit.etf.ba/get/b35621771d4ef09242865f6750140fad.jpg
if
[PLAIN]http://pokit.etf.ba/get/129fcaf8444d141b8e4df9ebb858ec4c.jpg

Homework Equations

The Attempt at a Solution

You may move this post if necessary but this is from my calculus courseware.

Now I don't want any of you to try and solve this for me. I am not lazy. The thing is, we have just started these differential equations. And to be honest, this is a jungle for me.

If any of you could just give me the directions, a little push forward I would be more than grateful.

Just the intuition, what is what and so on. I do know a bit how to solve the differential equations of this order. But these starting conditions bother me.

Please help me, and again i do not want a solution, I am posting this here not because I want this done, but because I want to understand.

Thank you

 

[LCKurtz]

What you have is a constant coefficient DE. You might review that topic. Here's a nice link to review it:

http://www.cliffsnotes.com/study_guide/Constant-Coefficients.topicArticleId-19736,articleId-19720.html

Once you have solved it you will need to apply your conditions.

[Edit] That shows how to solve the homogeneous equation. Try y = some constant for the NH equation to add to the general solution of the homegeneous equation before using the initial conditions.

 

[Bassalisk]

What you have is a constant coefficient DE. You might review that topic. Here's a nice link to review it:

http://www.cliffsnotes.com/study_guide/Constant-Coefficients.topicArticleId-19736,articleId-19720.html

Once you have solved it you will need to apply your conditions.

[Edit] That shows how to solve the homogeneous equation. Try y = some constant for the NH equation to add to the general solution of the homegeneous equation before using the initial conditions.

Thanks I will give it a shot. And our professor is "scaring us" with differential equations which have a non continuous domain. I will get back to that after I solve this problem.

 

[Bassalisk]

Hello, I solved the equation and got this soultion:

U_c=e^-x(C1cosx+c2sinx)+7

Now can you give me directions for those dependent and independent starting conditions. What does that mean in terms of differential equations?

 

[Bassalisk]

Homework Statement

Solve the differential equation(for voltage u_c(t) on the end of the capacitor in some electric circuit)
[PLAIN]http://pokit.etf.ba/get/402e740f4c35317784c20c0acd656de5.jpg
for independent starting conditions
[PLAIN]http://pokit.etf.ba/get/f840b445d268567428ada50ed466c4f6.jpg
and dependent starting conditions
[PLAIN]http://pokit.etf.ba/get/b35621771d4ef09242865f6750140fad.jpg
if
[PLAIN]http://pokit.etf.ba/get/129fcaf8444d141b8e4df9ebb858ec4c.jpg

Homework Equations

The Attempt at a Solution

Corrected