In Problems 7, 8, 9, and 10 the independent variable x is missing in the given differential equation. Proceed as in Example 2 and solve the equation by using the substitution u = y'. 7. yy' + (y')² + 1 = 0 Answer + 8. (y+1)y" = (y')² 9. y' + 2y(y')³ = 0 Answer 10. y'y" = y'
In Problems 7, 8, 9, and 10 the independent variable x is missing in the given differential equation. Proceed as in Example 2 and solve the equation by using the substitution u = y'. 7. yy' + (y')² + 1 = 0 Answer + 8. (y+1)y" = (y')² 9. y' + 2y(y')³ = 0 Answer 10. y'y" = y'
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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I want you to give me how question number 10 has this answer, make it simple as possible.
![The solution is
\[
y = \frac{1 + e^{cx - Cy + 1}}{C}
\]
This equation represents a mathematical expression where \( y \) is a function of \( x \), and other constants \( c \), \( C \), and possibly additional terms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5504642f-0145-4427-b5f2-66a9310e79bc%2Fbdd0715b-4f6a-4072-a1b1-a5bfe7ac009c%2Ffwb5lt_processed.png&w=3840&q=75)
Transcribed Image Text:The solution is
\[
y = \frac{1 + e^{cx - Cy + 1}}{C}
\]
This equation represents a mathematical expression where \( y \) is a function of \( x \), and other constants \( c \), \( C \), and possibly additional terms.
![In Problems 7, 8, 9, and 10, the independent variable \( x \) is missing in the given differential equation. Proceed as in Example 2 and solve the equation by using the substitution \( u = y' \).
7. \( yy'' + (y')^2 + 1 = 0 \)
[Answer ▼]
8. \( (y + 1)y'' = (y')^2 \)
9. \( y'' + 2y(y')^3 = 0 \)
[Answer ▼]
10. \( y^2 y'' = y' \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5504642f-0145-4427-b5f2-66a9310e79bc%2Fbdd0715b-4f6a-4072-a1b1-a5bfe7ac009c%2Ftpq0c4_processed.png&w=3840&q=75)
Transcribed Image Text:In Problems 7, 8, 9, and 10, the independent variable \( x \) is missing in the given differential equation. Proceed as in Example 2 and solve the equation by using the substitution \( u = y' \).
7. \( yy'' + (y')^2 + 1 = 0 \)
[Answer ▼]
8. \( (y + 1)y'' = (y')^2 \)
9. \( y'' + 2y(y')^3 = 0 \)
[Answer ▼]
10. \( y^2 y'' = y' \)
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