Question

Write the following ODEs as a system of first-order differential equations. (a) y" + 2y' + 3y = 0 (b) y"' + 2y" + y = 0

Answer 1

Answer:

a.$x'_2+2x_2+3 x_1=0$

b.$x'_2+2x_2+x_1=0$

Step-by-step explanation:

We are given differential equation of second order in each part

We have to change given differential equation into first order differential equation

a.y''+2y'+3y=0

Suppose $x_1=y(t)$

$x_2=y'(t)$

Differentiate w.r.t times then we get

$x'_1=y'(t)=x_2$

$x'_2=y''(t)$

Substitute the values in the given differential equation then we get

$x'_2+2x_2+3 x_1=0$

b.y''+2y'+y=0

Suppose

$x_1=y(t)$

$x_2=y'(t)$

Differentiate w.r.t time

Then we get

$x'_1=y'(t)=x_2$

$x'_2=y''(t)$

Substitute the values in given differential equation

$x'_2+2x_2+x_1=0$