Solve the equation. (x+ 3xy“) dx + e*y°dy = 0 Begin by separating the variables. Choose the correct answer below. y3 dy%3D 1+ 3y X Xp. et? OB. 1+ 3y* 4 dy x+3xy* dx D. The equation is already separated. An implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant. %3D (Type an expression using x and y as the variables.)
Solve the equation. (x+ 3xy“) dx + e*y°dy = 0 Begin by separating the variables. Choose the correct answer below. y3 dy%3D 1+ 3y X Xp. et? OB. 1+ 3y* 4 dy x+3xy* dx D. The equation is already separated. An implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant. %3D (Type an expression using x and y as the variables.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Solve the equation.**
\[
(x + 3xy^4) \, dx + e^{x^2} y^3 \, dy = 0
\]
---
**Begin by separating the variables. Choose the correct answer below.**
- **A.** \(\frac{y^3}{1 + 3y^4} \, dy = -\frac{x}{e^{x^2}} \, dx\)
- **B.** \(\frac{y^3}{1 + 3y^4} \, dx = -\frac{x}{e^{x^2}} \, dy\)
- **C.** \(\frac{dy}{dx} = -\frac{x + 3xy^4}{e^{x^2} y^3}\)
- **D.** The equation is already separated.
---
**An implicit solution in the form \( F(x, y) = C \) is** \(\boxed{}\) **= C, where C is an arbitrary constant.**
*(Type an expression using x and y as the variables.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02c9694f-8959-437e-bd84-546c9a464c26%2F912bfe91-f181-4df6-b227-cb5b624b0372%2Farmkamn_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve the equation.**
\[
(x + 3xy^4) \, dx + e^{x^2} y^3 \, dy = 0
\]
---
**Begin by separating the variables. Choose the correct answer below.**
- **A.** \(\frac{y^3}{1 + 3y^4} \, dy = -\frac{x}{e^{x^2}} \, dx\)
- **B.** \(\frac{y^3}{1 + 3y^4} \, dx = -\frac{x}{e^{x^2}} \, dy\)
- **C.** \(\frac{dy}{dx} = -\frac{x + 3xy^4}{e^{x^2} y^3}\)
- **D.** The equation is already separated.
---
**An implicit solution in the form \( F(x, y) = C \) is** \(\boxed{}\) **= C, where C is an arbitrary constant.**
*(Type an expression using x and y as the variables.)*
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