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General solution to a second order homogeneous differential equation

  • #1

Homework Statement



Find if it is true that the general solution to : y'' - y' = 0, where y(x),
can be written as : y(x) = c1 cosh(x) + c2 sinh(x), where c1 and c2 are real
arbitrary constants.

Homework Equations



differential equation solving

The Attempt at a Solution



I just want to know what the h's mean at the end of sin and cos.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
The 'h' means hyperbolic. cosh(x)=(e^x+e^(-x))/2. sinh(x)=(e^x-e^(-x))/2. That's all, it's just an abbreviation for those expressions. Can you show they both satisfy your differential equation?
 

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