Mathematics: Guess a solution to y + y + y = 5.

4/5, 2, 2.3, 2.65/48, 3/16, 0.5, 0.751/5, 0.35, 12/25, 0.5, 4/5-3/4, -7/10, 3.4, 8/10...

Guess a solution to y + y + y = 5. - id51097226, 27lcasselberry

jskdkfjf

13.03.2022

general solution= $e^{-\frac{1}{2} x}(Acos\frac{3}{2} x+Bsin\frac{3}{2}x)$ +5

Step-by-step explanation:

using linear differential equation method

y'' + y' + y = 5

writing down the characteristics equation.

m^2+m+1=0

using quadratic formula

$m=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

we get

$m=\frac{-1\pm \sqrt{1^2-4(1)(1)}}{2(1)}$

$m=-\frac{1}{2} \pm \frac{3}{2} i$

now Complementary function(CF)

$y=e^{ax}(Acosbx+Bsinbx)\\y=e^{-\frac{1}{2} x}(Acos\frac{3}{2} x+Bsin\frac{3}{2}x)$

now for particular integrals

$D^2y+Dy+y=5\\(D^2+D+1)y=5\\y=\frac{5}{D^2+D+1}$

$P.I.=\frac{5\times e^{0x} }{D^2+D+1}$

putting D=0

we get

P.I.=5

general solution=CF+PI

general solution= $e^{-\frac{1}{2} x}(Acos\frac{3}{2} x+Bsin\frac{3}{2}x)$ +5

0,0(0 оценок)