Linear Differential Equations, no x in p(x) or q(x)?

[rygza]

An integrating factor e^(integral p(x) ) can be used to solve Linear D.E. in form y' + P(x)y=Q(x), but what do i do when there is no x in P(x) or Q(x)?

for instance in these problems: #1)y' - y=4(e^x) #2)y'+2xy=4

Is it wrong to use P(x)= -1 for problem 1, and Q(x)=4 for problem 2?

This is what I've been using but I can't check if it's right (answer not in back of book).

 

[adriang]

1) p(x)=-1, q(x)=4e^x & 2) p(x)=2x and q(x)=4 ( Just because there's no x doesn't mean its not a function of x, or of whatever independent variable your working with; its just for every x value u'll get the same f(x), which is obv since its constant. you can view it as f(x)=4x^0, whatever x you use you'll get 4)

 

[rygza]

1) p(x)=-1, q(x)=4e^x & 2) p(x)=2x and q(x)=4 ( Just because there's no x doesn't mean its not a function of x, or of whatever independent variable your working with; its just for every x value u'll get the same f(x), which is obv since its constant.)

hmm i see. Thanks for the clarification