In Problems 1-6 solve the given Bernoulli equation. dy dx 1. x 3. dy dx dy dx 5. x² dy dx 7. x². 11. + y y² = y(xy³ - 1) dy dx dy dx + y² = xy 9. xy(1 + xy²) = 1, = = 2xy = 3y4, y(1) = In Problems 7-10 solve the given differential equation subject to the indicated initial condition. dy dx 1 2 y(1) = 0 -2-y + y², y₁ = 2 2. 4. x - y = exy² dy dx - 10. 2 dy 6. 3(1 + x²) = 2xy(³1) dx 8. y¹/2 dy dx (1 + x)y = xy² y(1) = 1 In Problems 11-16 solve the given Ricatti equation; y₁ is a known solution of the equation. = + y³/2 = 1, y(0) = 4 dy y dx X
In Problems 1-6 solve the given Bernoulli equation. dy dx 1. x 3. dy dx dy dx 5. x² dy dx 7. x². 11. + y y² = y(xy³ - 1) dy dx dy dx + y² = xy 9. xy(1 + xy²) = 1, = = 2xy = 3y4, y(1) = In Problems 7-10 solve the given differential equation subject to the indicated initial condition. dy dx 1 2 y(1) = 0 -2-y + y², y₁ = 2 2. 4. x - y = exy² dy dx - 10. 2 dy 6. 3(1 + x²) = 2xy(³1) dx 8. y¹/2 dy dx (1 + x)y = xy² y(1) = 1 In Problems 11-16 solve the given Ricatti equation; y₁ is a known solution of the equation. = + y³/2 = 1, y(0) = 4 dy y dx X
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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Can someone help me solve these problems please I’m having a difficult time .5 and 7
Transcribed Image Text:Depo Answers to odd-numbered problems begin on page A-3.
In Problems 1–6 solve the given Bernoulli equation.
dy
dy
dx
dx
1. x
3.
dy
dx
+y
dy
5. x² + y² = xy
dx
7. x²-
11.
1
y²
= y(xy³ - 1)
dy
dx
2xy = 3y¹, y(1) = 1/2
dy
9. xy(1 + xy²) 1, y(1) = 0
dx
dy
dx
2.
4. x
In Problems 7–10 solve the given differential equation subject to the
indicated initial condition.
dy
dx
y = exy²
1
10. 2
(1 + x)y = xy²
dy
6. 3(1 + x²). = 2xy (³1)
dx
dy
8. y¹/2 +y³/2 = 1, y(0) = 4
dx
y(1) = 1
In Problems 11-16 solve the given Ricatti equation; y₁ is a known solution
of the equation.
-2-y + y², y₁ = 2
dy
y X
dx X y²
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