Lecture
A linear first-order equation is an equation that is linear with respect to the function y and its derivative y ' .
It looks like:
y ' = p ( x ) · y + q ( x ),
where p ( x ) and q ( x ) are given continuous or constant functions.
The solution of the linear equation is sought in the form y = u ( x ) · v ( x ) . The functions u ( x ) and v ( x ) are found from equations with separable variables:
a) v ' = p ( x ) · v ;
b) u '· v ( x ) = q ( x ) .
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Mathematical analysis. Differential equations
Terms: Mathematical analysis. Differential equations