Second order differentiel equations

Gamestops

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Hey everybody

So I'm fairly new to differential equations and this is my first time dealing with one of second order. Therefore if the problem seems easy that's why.

I am supposed to rewrite or reduce the following equation to a system of 1. order differential equations

y''-0.1*y+2=0

and then find a numerical solution where the following is true
y(0)=10 and y'(0)=-1

I'm not necessarily looking for a solution, but rather if someone could forward me to some kind guide or lesson about this.
 
Last edited:
Hey everybody

So I'm fairly new to differentiel equations and this is my first time dealing with one of second order. Therefore if the problem seems easy thats why.

I am supposed rewrite or reduce the following equation to a system of 1. order differentiel equations

y''*0,1*y+2=0 ................... What does that mean?

and then find a numerical solution where the following is true
y(0)=10 and y'(0)-1

i'm not necessarily looking for a solution, but rather if someone could forward me to some kind guide or lesson about this.
.
 
Oh sorry forgot to convert it to american notation

it should say y''-0.1*y+2=0
 
Hey everybody

So I'm fairly new to differential equations and this is my first time dealing with one of second order. Therefore if the problem seems easy that's why.

I am supposed to rewrite or reduce the following equation to a system of 1. order differential equations

y''-0.1*y+2=0

and then find a numerical solution where the following is true
y(0)=10 and y'(0)=-1

I'm not necessarily looking for a solution, but rather if someone could forward me to some kind guide or lesson about this.
Z^2-0.1=0
y=C1exp(0.1x)+C2exp(-0.1x)
y(0)=C1+C2=10 (1)
y'(0)=0.1*C1-0.1*C2=-1 or y'(0)=C1-C2=-10 (2)
(1) and (2) => C1=0 C2=10
y= 10*exp(-0.1x)
 
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