§1.7 LINEAR EQUATIONS PROBLEM SET 1.7 In problems 1 - 6, solve each linear equation. State an interval on which the general solution is defined. dy 1. +y = ³ dx 2. x²y + xy = 1 3. xdy = (xsin x - y)dx 4. cos r- + y sin x = 1 dy dx 5. cos a sin zdy + (y cos³x - 1)dx = 0 6. ydx-4(x+y)dy = 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Stuck on problems 5 and 6

§1.7 - LINEAR EQUATIONS
In problems 1 - 6, solve each linear equation. State an interval on which the general solution is
defined.
dy
dr
+y=e³r
2. r²y + xy = 1
3. zdy = (xsin x - y)dr
dy
1.
4. cos r
+ y sin x = 1
dx
5. cos²xsin ady+ (y cos³x - 1)dx = 0
6. ydx-4(x + y)dy = 0
7.
In problems 7-9, solve the given differential equation subject to the indicated initial condition.
dy
dr
+ 5y = 20, y(0) = 2.
PROBLEM SET 1.7
di
8. L + Ri= E, i(0) = io. Note that L, R, and E are constants.
dt
-1.
9. y' + (tan x)y = cos²x, y(0) = −
Transcribed Image Text:§1.7 - LINEAR EQUATIONS In problems 1 - 6, solve each linear equation. State an interval on which the general solution is defined. dy dr +y=e³r 2. r²y + xy = 1 3. zdy = (xsin x - y)dr dy 1. 4. cos r + y sin x = 1 dx 5. cos²xsin ady+ (y cos³x - 1)dx = 0 6. ydx-4(x + y)dy = 0 7. In problems 7-9, solve the given differential equation subject to the indicated initial condition. dy dr + 5y = 20, y(0) = 2. PROBLEM SET 1.7 di 8. L + Ri= E, i(0) = io. Note that L, R, and E are constants. dt -1. 9. y' + (tan x)y = cos²x, y(0) = −
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