EXERCISES 2.2 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^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)
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21 dy = sin(x) dx Divide both sides by 21 and sin(x) to get dy/sin(x) = dx/21. Integrate both sides to get -cos(x) = x/21 + C. 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^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.
EXERCISES 2.2 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)
Solve the differential equations in Exercises $9-22$ $$\frac{d y}{d x}=\sqrt{y} \cos ^{2} \sqrt{y}$$
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