1. ## differential equation of y''+y'-6y =0 is my answer correct

find the general solution of the differential equation y''+y'-6y =0
y''+y'-6y

m² + m - 6 = 0
m-2(m+3)=0
m-2=0m-3=0
m-2=0m+3=0

yᶜ = C₁℮^(-3x) + C₂℮^(2x)

find the particular solution of
y''+y'-6y =0 given that y(0)= 5 and y'(0)=0 getting trouble with this part help please

2. ## Re: differential equation of y''+y'-6y =0 is my answer correct

find the general solution of the differential equation y''+y'-6y =0
y''+y'-6y

m² + m - 6 = 0
m-2(m+3)=0
m-2=0m-3=0
m-2=0m+3=0

yᶜ = C₁℮^(-3x) + C₂℮^(2x)

find the particular solution of
y''+y'-6y =0 given that y(0)= 5 and y'(0)=0 getting trouble with this part help please
$y(x) = C_1 e^{-3x}+C_2 e^{2x}$

$y^\prime(x)= -3C_1 e^{-3x} + 2 C_2 e^{2x}$

$y(0) = 5 = C_1+C_2$

$y^\prime(0) = 0 = -3C_1 + 2 C_2$

$C_2 = \dfrac 3 2 C_1$

$\dfrac 5 2 C_1 = 5$

$C_1 = 2, C_2 = 3$

$y(x) = 2 e^{-3x} + 3 e^{2x}$

3. ## Re: differential equation of y''+y'-6y =0 is my answer correct

oh wow i had i right all along i had the 3/2 5/2 . thanks alot

4. ## Re: differential equation of y''+y'-6y =0 is my answer correct

Find the general solution of: .$\displaystyle y'' +y'-6y \:=\:0$

$\displaystyle m^2 + m - 6 \:=\: 0 \quad\Rightarrow\quad (m-2)(m+3)\:=\:0 \quad\Rightarrow\quad m \:=\:2,-3$

$\displaystyle y \:=\: C_{_1} e^{2x} + C_{_2} e^{-3x}$

This is correct!

Find the particular solution of $\displaystyle y''+y'-6y \:=\:0$
given that $\displaystyle y(0)= 5$ and $\displaystyle y'(0)=0$

You have: .$\displaystyle y(x) \;=\;C_{_1}e^{2x} + C_{_2}e^{-3x}$

We are told that $\displaystyle y(0) = 5.$

. . $\displaystyle C_{_1}e^0 + C_{_2}e^0 \:=\:5 \quad\Rightarrow\quad \bf{\color{red}C_1 + C_2 \:=\:5}$

We have: .$\displaystyle y'(x) \:=\:2C_{_1}e^{2x} -3C_{_2}e^{-3x}$

We are told that $\displaystyle y'(0) = 0.$

. . $\displaystyle 2C_{_1}e^0 -3C_{_2}e^0 \:=\:0 \quad\Rightarrow\quad \bf{\color{red}2C_1 - 3C_2 \:=\:0}$

Solve the system of equations: .$\displaystyle C_1 = 3,\;C_2 = 2$

Therefore: .$\displaystyle y \;=\;3e^{2x} + 2e^{-3x}$

Um ... too slow!
.

5. ## Re: differential equation of y''+y'-6y =0 is my answer correct

find the general solution of the differential equation y''+y'-6y =0
y''+y'-6y

m² + m - 6 = 0
m-2(m+3)=0

You need to be more careful how you write things. (m- 2)(m+ 3)= m²+ m- 6 but m-2(m+ 3)= m- 2m- 6= -m- 6.

m-2=0m-3=0
m-2=0m+3=0
And here you need spaces to make it clear that these are two separate equations:
m- 2= 0 and m+ 3= 0 (NOT "m- 3= 0"!)

yᶜ = C₁℮^(-3x) + C₂℮^(2x)

find the particular solution of
y''+y'-6y =0 given that y(0)= 5 and y'(0)=0 getting trouble with this part help please

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# y"-y'-6y=0 homogenous differential

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