Verify that the given differential equation is éxáct; then solve it. 3y2 dx + 4x2 2y 5 dy = 0 Vy 8x x4 y2
Verify that the given differential equation is éxáct; then solve it. 3y2 dx + 4x2 2y 5 dy = 0 Vy 8x x4 y2
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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![**11.** Verify that the given differential equation is exact; then solve it.
\[
\left( \frac{8x}{y} - \frac{3y^2}{x^4} \right) dx + \left( \frac{2y}{x^3} - \frac{4x^2}{y^2} + \frac{5}{\sqrt{y}} \right) dy = 0
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- ☐ A. The equation is exact and an implicit solution in the form \( F(x,y) = C \) is \_\_\_\_\_\_\_\_ = \( C \),
where \( C \) is an arbitrary constant.
(Type an expression using \( x \) and \( y \) as the variables.)
- ☐ B. The equation is not exact.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F215c9956-76b8-4988-9874-46d947288784%2Fd6fb31c4-409d-45c0-85c3-3e351f021a01%2Fa4ua349_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**11.** Verify that the given differential equation is exact; then solve it.
\[
\left( \frac{8x}{y} - \frac{3y^2}{x^4} \right) dx + \left( \frac{2y}{x^3} - \frac{4x^2}{y^2} + \frac{5}{\sqrt{y}} \right) dy = 0
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- ☐ A. The equation is exact and an implicit solution in the form \( F(x,y) = C \) is \_\_\_\_\_\_\_\_ = \( C \),
where \( C \) is an arbitrary constant.
(Type an expression using \( x \) and \( y \) as the variables.)
- ☐ B. The equation is not exact.
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To prove the differential equation is exact and find its implicit solution.
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