Question
We are learning how to solve systems of linear ODE's by elimination. I am not sure how to solve this:
x'=-y+t
y'=x-t
I took the derivative of the second eqn to get
y''-x'=-t'
and added the two to get
y''+y=-t'+t
but I don't think thats the right way to proceed. Suggestions?
tia
x'=-y+t
y'=x-t
I took the derivative of the second eqn to get
y''-x'=-t'
and added the two to get
y''+y=-t'+t
but I don't think thats the right way to proceed. Suggestions?
tia
Answers
x'=-y+t
y'=x-t
Add these two equations, you get:
x' + y' = x - y
y' + (x')y = x
That gives you a linear differential equation of the form:
y' + Py = Q
Considering that P is the derivative of x, it'll make things easy while solving for the integrating factor.
y'=x-t
Add these two equations, you get:
x' + y' = x - y
y' + (x')y = x
That gives you a linear differential equation of the form:
y' + Py = Q
Considering that P is the derivative of x, it'll make things easy while solving for the integrating factor.
The equation should be:
x' + y' = x - y
=> y' + (1)y = (x - x')
x' + y' = x - y
=> y' + (1)y = (x - x')
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