# Math Help - First order linear Differential eq

1. ## First order linear Differential eq

1. Find the solution to 2y'+y=x that goes through (-1;e-3)

2. The Functions y(x) = lnx och x(v)=cosv, determine dy/dv

How do I solve these problems?

2. Originally Posted by mayth
1. Find the solution to 2y'+y=x that goes through (-1;e-3)
You need to use the integrating factor method. Firstly divide the equation through by 2 to give...

$y'+\frac{1}{2}y=\frac{x}{2}$

the condition (-1,e-3) will be used to solve the constant of integration once finished.

Here is a different D.E solved with the integrating factor method. Have a look.

http://www.mathhelpforum.com/math-he...equations.html

3. Originally Posted by mayth
2. The Functions y(x) = lnx och x(v)=cosv, determine dy/dv
What are you tring to say here?