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Solve the differential equations in Exercises 5-12. 5. y' = 2x?y – 4y 6. e* y dx+4y³ dy = 0

Solve the differential equations in Exercises 5-12. 5. y' = 2x?y – 4y 6. e* y dx+4y³ dy = 0

Advanced Engineering Mathematics
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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Number 5 and 9
+ 2xy 4. sin xy' = xy +4x %3D dx Solve the differential equations in Exercises 5-12. 5. y' = 2x?y- 4y 6. e* y dx+4y³ dy = 0 dy 7. (x2 + 1) = xy² +x dx 8. sec xy' – xy/(y +4) = 0 9. e* (y² – 4y) dx +4 dy = 0 xy³ +3xy³ 2x²y eadon dy 10. dx dy 11. t dt dy = te dt dr 12. (r2 + 1) cos 0 =r sin 0 de Solve the initial value problems in Exercises 13-16. 13. y' + x2/y = 0, y(0) = 1 dy 14. 3 = 2xy- y, y(2) = 1 dx dy 15. dx 4ху y(1) = 1 y2 +4' 3.3 EXACT DIFFERENTIAL EQUATIC In the last section we learned how to sc we will consider a type of equation w If we use the Chain Rule to differentis implicitly with respect to x, d F(x, y):
Transcribed Image Text:+ 2xy 4. sin xy' = xy +4x %3D dx Solve the differential equations in Exercises 5-12. 5. y' = 2x?y- 4y 6. e* y dx+4y³ dy = 0 dy 7. (x2 + 1) = xy² +x dx 8. sec xy' – xy/(y +4) = 0 9. e* (y² – 4y) dx +4 dy = 0 xy³ +3xy³ 2x²y eadon dy 10. dx dy 11. t dt dy = te dt dr 12. (r2 + 1) cos 0 =r sin 0 de Solve the initial value problems in Exercises 13-16. 13. y' + x2/y = 0, y(0) = 1 dy 14. 3 = 2xy- y, y(2) = 1 dx dy 15. dx 4ху y(1) = 1 y2 +4' 3.3 EXACT DIFFERENTIAL EQUATIC In the last section we learned how to sc we will consider a type of equation w If we use the Chain Rule to differentis implicitly with respect to x, d F(x, y):
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