EXERCISES 2.3 In Problems 1-24 find the general solution of the given differential equation. Give the largest interval I over which the general solution is defined. Determine whether there are any transient terms in the general solution. 1. dy/dx = 5y 2. dy/dx + 2y = 0 3. dy/dx + y = e^3x 4. 3 dy/dx + 12y = 4 5. y' + 3x^2y = x^2 6. y' + 2xy = x^3 7. x^2y' + xy = 1 8. y' = 2y + x^2 + 5 9. x dy/dx - y = x^2 sin x 10. x dy/dx + 2y = 3 11. x dy/dx + 4y = x^3 - x 12. (1 + x) dy/dx - xy = x + x^2 13. x^2y' + x(x + 2)y = e^x 14. xy' + (1 + x)y = e^x sin 2x 15. y dx - 4(x + y^6) dy = 0
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The given differential equation is: \[ \frac{dy}{dx} + 2 = 0 \] Show more…
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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^x y 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^3 3x dy = 0 13. (e^y + 1)^2 e^-y dx + (e^x + 1)^3 e^-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)
Madhur L.
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)^2/(4x+5)^2 11. csc y dx + sec^2 x dy = 0 12. sin 3x dx + 2y cos^3 3x dy = 0 13. (e^y + 1)^2 e^-y dx + (e^x + 1)^3 e^-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)
Sri K.
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)
Christy G.
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