1.8 - Solve the following ordinary differential equations, and specify how many and what kind of boundary conditions are needed. Identify dependent and independent variables. d а) dr `r dr (1d(rc), = 0 b) у - 2у -8у %3 хе* +4 2х с) у 1+x? V =1 1.9 - Solve the following O.D.E y +4y +5y = 8 а) y(0) = 2, y'(0) =-5 b) x²y" +xy' +9x²y=0 (Find the general solution) 1.10 - Show the solution to the following differential equation: d²y x dy dx? = 0 2 dx y(0) = 1, y(0) = 0 is y = erfc) 2 where erfc(x) e do
1.8 - Solve the following ordinary differential equations, and specify how many and what kind of boundary conditions are needed. Identify dependent and independent variables. d а) dr `r dr (1d(rc), = 0 b) у - 2у -8у %3 хе* +4 2х с) у 1+x? V =1 1.9 - Solve the following O.D.E y +4y +5y = 8 а) y(0) = 2, y'(0) =-5 b) x²y" +xy' +9x²y=0 (Find the general solution) 1.10 - Show the solution to the following differential equation: d²y x dy dx? = 0 2 dx y(0) = 1, y(0) = 0 is y = erfc) 2 where erfc(x) e do
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
I'm stuck with problem 1.8 and 1.9. I'd appreciate a step by step solution. Thanks!
![1.8 - Solve the following ordinary differential equations, and specify how many and what
kind of boundary conditions are needed. Identify dependent and independent variables.
d 1
а)
dr `r dr
2) 0
b) у - 2у - 8y%3D хе" + 4
2x
c) y'.
1+x
y =1
1.9 - Solve the following O.D.E
y' +4y +5y= 8
а)
y(0) = 2, y'(0) =-5
||
b) x²y' +xy +9x²y=0
(Find the general solution)
1.10 - Show the solution to the following differential equation:
dy, x dy
+
dx?
2 dx
y(0) = 1, y(0) = 0
is y = erfc()
where erfc(x) =-
02
e
de](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf3f2c9a-abad-480f-b86a-b3c402154b98%2F5f96541b-0cac-4d8a-9f8a-7d2383720269%2Fcijnoni_processed.png&w=3840&q=75)
Transcribed Image Text:1.8 - Solve the following ordinary differential equations, and specify how many and what
kind of boundary conditions are needed. Identify dependent and independent variables.
d 1
а)
dr `r dr
2) 0
b) у - 2у - 8y%3D хе" + 4
2x
c) y'.
1+x
y =1
1.9 - Solve the following O.D.E
y' +4y +5y= 8
а)
y(0) = 2, y'(0) =-5
||
b) x²y' +xy +9x²y=0
(Find the general solution)
1.10 - Show the solution to the following differential equation:
dy, x dy
+
dx?
2 dx
y(0) = 1, y(0) = 0
is y = erfc()
where erfc(x) =-
02
e
de
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