Write the following ODEs as a system of first-order differential equations. (a) y" + 2y' + 3y = 0 (b) y"' + 2y" + y = 0
Accepted Solution
A:
Answer:a.[tex]x'_2+2x_2+3 x_1=0[/tex]b.[tex]x'_2+2x_2+x_1=0[/tex]Step-by-step explanation:We are given differential equation of second order in each partWe have to change given differential equation into first order differential equationa.y''+2y'+3y=0Suppose [tex]x_1=y(t)[/tex][tex]x_2=y'(t)[/tex]Differentiate w.r.t times then we get [tex]x'_1=y'(t)=x_2[/tex][tex]x'_2=y''(t)[/tex]Substitute the values in the given differential equation then we get [tex]x'_2+2x_2+3 x_1=0[/tex]b.y''+2y'+y=0Suppose [tex]x_1=y(t)[/tex][tex]x_2=y'(t)[/tex]Differentiate w.r.t time Then we get [tex]x'_1=y'(t)=x_2[/tex][tex]x'_2=y''(t)[/tex]Substitute the values in given differential equation[tex]x'_2+2x_2+x_1=0[/tex]