Question

Diff EQ.
Solution of y''+9y'=0 y(0)=1 y'(0)=1 ?

Answer 1

Can't use euler-cauchy method. So only way left is just the euler method, but there's no initial value "h" to use euler.

Answer 2

I figured out how to this one, How bout this one?
y''+9y'=0 y(0)=1 y'(0)=1.

Answer 3

Could someone explain the euler formula and how to use it, with...
y''+9y'=0 y(0)=1 y'(0)=1.

Answer 4

\[y(x)=\frac{10}{9}-\frac{e^{-9 x}}{9} \]

Answer 5

Okay.... Could you explain the logic behind your answer.

Answer 6

They want an exact solution. "Solve"

Answer 7

\[y(x)\to c_2-\frac{1}{9} c_1 e^{-9 x} \ ? \]

Answer 8

Used Mathematica v9 to solve the equation.
I can delete all of my postings related to this problem if you wish.

Answer 9

\[y \prime \prime+9y \prime =0\]
integrate w.r.t.x
\[y \prime+9y=c\]
when x=0,y=1,y'=1
1+9(1)=c
c=10
y'+9y=10
\[I.F.=e ^{\int\limits 9~dx}=e ^{9x}\]
C.S. is
\[y e ^{9x}=\int\limits 10~e ^{9x}dx+C\]
\[ye ^{9x}=\frac{ 10 e ^{9x} }{ 9 }+C\]
again~when~x=0,y=1
\[1(1)=\frac{ 10(1) }{ 9 }+C,C=1-\frac{ 10 }{ 9 }=-\frac{ 1 }{ 9 }\]
C.S.is
\[y e ^{9x}=\frac{ 10e ^{9x} }{ 9 }-\frac{ 1 }{ 9 }\]