Solving the Initial Value Problem for 'y' = x, x' = -5y-4x

[Ry122]

y' = x
x' = -5y-4x

y(0) = 1
x(0) = 0

after finding the general solution as shown here
http://www.wolframalpha.com/input/?i=y'+=+x,+x'+=+-5y-4x

how do you go about applying the initial values and finding the complete solution?

 

[HallsofIvy]

Your general solution should have two undetermined coefficients. Substitute 0 for t, set x= 0, y= 1 and you will have two equations to solve for the two coefficients.

 

[Ry122]

actually I don't think wolfram alpha has done the correct thing in making x and y a function of t as there's no mention of another variable in the original equations. What would you do when they aren't functions of t?

 

[HallsofIvy]

You can call the independent variable whatever you want! What did you mean by x' and y'? I assumed the primes were derivatives. With respect to what variable?