Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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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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Step 1

Given that

(8xy-3y2x4)dx+(2yx3-4x2y2+5y)dy=0

To prove the differential equation is exact and find its implicit solution.

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