2nd Order Homogeneous, Real Roots, Initial Value

[Destroxia]

Homework Statement

Solve the initial value problem

Homework Equations

Quadratic Formula

The Attempt at a Solution

My problem is that I don't understand how to solve the constants now, I understand, 2 equations, 2 unknowns, but when I plug the y(0) = 0 into the YsubH equation, everything cancels out, I can't solve for anything. I don't see anyway to cancel anything in the equations either to make it not equivalent to 0, or to be able to solve it.

[/B]

 

[Mark44]

Homework Statement

Solve the initial value problem

For simple differential equations such as this, it's better to type the equation and initial condition than to post an image. What I see is a thumbnail that shows "0, y". I have to click the image to see the full image.

Your equation is
2y'' + y' - 4y = 0, y(0) = 0, y'(0) = 1

Homework Equations

Quadratic Formula

The Attempt at a Solution

My problem is that I don't understand how to solve the constants now, I understand, 2 equations, 2 unknowns, but when I plug the y(0) = 0 into the YsubH equation, everything cancels out, I can't solve for anything. I don't see anyway to cancel anything in the equations either to make it not equivalent to 0, or to be able to solve it.
[/B]

Your solution looks fine to me. Your error is in how you evaluated it. Note that e⁰ = 1, so you get $c_1 + c_2 = 0$ for your first equation, so everything does not cancel out.

 

[Destroxia]

For simple differential equations such as this, it's better to type the equation and initial condition than to post an image. What I see is a thumbnail that shows "0, y". I have to click the image to see the full image.

Your equation is
2y'' + y' - 4y = 0, y(0) = 0, y'(0) = 1

Your solution looks fine to me. Your error is in how you evaluated it. Note that e⁰ = 1, so you get $c_1 + c_2 = 0$ for your first equation, so everything does not cancel out.

Okay, I'll remember that, the next time that I post... and thank you so much for catching my error, I feel terrible that I made such an algebra mistake...