Question

In Problems 1–22 solve the given differential equation by separation of variables. 1. dy/dx = sin 5x 2. dy/dx = (x + 1)^2 3. dx + e^3x dy = 0 4. dy – (y – 1)^2 dx = 0 5. x dy/dx = 4y 6. dy/dx + 2xy^2 = 0 7. dy/dx = e^3x+2y 8. e^xy dy/dx = e^-y + e^-2x-y 9. y ln x dx/dy = ((y + 1)/x)^2 10. dy/dx = ((2y + 3)/(4x + 5))^2 11. csc y dx + sec^2x dy = 0 12. sin 3x dx + 2y cos^3x dy = 0 13. (e^y + 1)^2e^-y dx + (e^x + 1)^3e^-x dy = 0 14. x(1 + y^2)^1/2 dx = y(1 + x^2)^1/2 dy 15. dS/dr = kS 16. dQ/dt = k(Q – 70) 17. dP/dt = P – P^2 18. dN/dt + N = Nte^t+2 19. dy/dx = (xy + 3x – y – 3) / (xy – 2x + 4y – 8) 20. dy/dx = (xy + 2y – x – 2) / (xy – 3y + x – 3)

          In Problems 1–22 solve the given differential equation by separation of variables.

1. dy/dx = sin 5x
2. dy/dx = (x + 1)^2
3. dx + e^3x dy = 0
4. dy – (y – 1)^2 dx = 0
5. x dy/dx = 4y
6. dy/dx + 2xy^2 = 0
7. dy/dx = e^3x+2y
8. e^xy dy/dx = e^-y + e^-2x-y
9. y ln x dx/dy = ((y + 1)/x)^2
10. dy/dx = ((2y + 3)/(4x + 5))^2
11. csc y dx + sec^2x dy = 0
12. sin 3x dx + 2y cos^3x dy = 0
13. (e^y + 1)^2e^-y dx + (e^x + 1)^3e^-x dy = 0
14. x(1 + y^2)^1/2 dx = y(1 + x^2)^1/2 dy
15. dS/dr = kS
16. dQ/dt = k(Q – 70)
17. dP/dt = P – P^2
18. dN/dt + N = Nte^t+2
19. dy/dx = (xy + 3x – y – 3) / (xy – 2x + 4y – 8)
20. dy/dx = (xy + 2y – x – 2) / (xy – 3y + x – 3)

In Problems 1–22 solve the given differential equation by separation of variables.

1. dy/dx = sin 5x
2. dy/dx = (x + 1)^2
3. dx + e^3x dy = 0
4. dy – (y – 1)^2 dx = 0
5. x dy/dx = 4y
6. dy/dx + 2xy^2 = 0
7. dy/dx = e^3x+2y
8. e^xy dy/dx = e^-y + e^-2x-y
9. y ln x dx/dy = ((y + 1)/x)^2
10. dy/dx = ((2y + 3)/(4x + 5))^2
11. csc y dx + sec^2x dy = 0
12. sin 3x dx + 2y cos^3x dy = 0
13. (e^y + 1)^2e^-y dx + (e^x + 1)^3e^-x dy = 0
14. x(1 + y^2)^1/2 dx = y(1 + x^2)^1/2 dy
15. dS/dr = kS
16. dQ/dt = k(Q – 70)
17. dP/dt = P – P^2
18. dN/dt + N = Nte^t+2
19. dy/dx = (xy + 3x – y – 3) / (xy – 2x + 4y – 8)
20. dy/dx = (xy + 2y – x – 2) / (xy – 3y + x – 3)

Added by Anthony C.

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