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 whatkind of boundary conditions are needed. Identify dependent and independent variables.d 1а)dr `r dr2) 0b) у - 2у - 8y%3D хе" + 42xc) y'.1+xy =11.9 - Solve the following O.D.Ey' +4y +5y= 8а)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 dxy(0) = 1, y(0) = 0is y = erfc()where erfc(x) =-02ede

As per bartleby guidelines, for more than one question asked, only one is to be answered, kindly…

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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Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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

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