Total points: 65 1. Explain what is meant by the phrase "first-order differential equation." 2. Determine whether each of the functions below is a solution of the differential equation ys-t-y=0? (4...

Sol:
First – order differential equation or an ordinary differential equation is an equation containing
a function of one independent variable and its derivatives.
Sol:
( )
the characteristic equation is , whose roots are .
Hence the general solution of the given equation is
Sol:
a. Integrating factor = (∫ )
Multiplying it on both sides, we get,




( )



Integrating on both sides, we get,
∫



( )

( )


Given ( )
( )

( )


b.
Integrating on both sides, we get,
∫



Given ( )



( )



Sol:
( )

√

Consider the function, ( )

√
...