please send handwritten solution for Q 25 1.6 1.6 ProblemsFind general solutions of the differential equations in Prob-lems i through 30. Primes denote derivatives with respect to xthroughout.15. x(x + y)y' + y(3x + y) = 016. y = Vx + y +118. (x + y)y = 120. y?y' + 2xy = 6x22. x'y + 2xy = 5y*24. 2xy' + y'e-24 = 2xy25. y?(xy' + y)(1 +x*)/2 = x26. 3y?y' + y' = e*27. 3xyy = 3x* + y28. xe' y = 2(e +x'e)29. (2x sin y cos y)y' 4x +sin' y30. (x +e)y' = xe – 117. y = (4x + y)?19. xy' + 2ry 5y21. y' = y + y23. xy' + 6y = 3xyt/31. (x + y)y = x - y3. xy = y +2xy5. x(x+ y)y' = y(x – y) 6. (x + 2y)y' y7. xy'y' = x + y9. x'y = xy + y11. (x² – y?)y = 2ry12. xyy' = y? + x/4x? + y?13. xy = y +Vr + y?14. yy +x = x² + y?2. 2xyy' = x? + 2y?4. (x - y)y' = x+ y%3D8. x'y' = xy + x'erla10. xyy' = x? +3y?1.6 Substitution Methods and Exact Equations 73In Problems 31 through 42, verify that the given differentialequation is exact; then solve it.60. Use the method in Problem 59 to solve the differentialequationdy2y-x +731. (2x + 3y) dx + (3x +2y) dy = 032. (4x - y) dx + (6y – x) dy = 033. (3x? +2y?) dx+ (4xy +6y?) dy = 034. (2xy + 3x?) dx + (2x'y+4y) dy = 035. (x' +2) dx + (y² + In x) dy = 0dx 4x – 3y – 1861. Make an appropriate substitution to find a solution of theequation dy/dx = sin(x – y). Does this general solutioncontain the linear solution y(x) = x - 1/2 that is readilyverified by substitution in the differential equation?62. Show that the solution curves of the differential equation36. (1 + ye") dx + (2y + xe) dy = 0y(2r - y)x(2y3 - x)37. (cos x + In y) dx +dy = 0dydx

Question

please send handwritten solution for Q 25 1.6 1.6 ProblemsFind general solutions of the differential equations in Prob-lems i through 30. Primes denote derivatives with respect to xthroughout.15. x(x + y)y' + y(3x + y) = 016. y = Vx + y +118. (x + y)y = 120. y?y' + 2xy = 6x22. x'y + 2xy = 5y*24. 2xy' + y'e-24 = 2xy25. y?(xy' + y)(1 +x*)/2 = x26. 3y?y' + y' = e*27. 3xyy = 3x* + y28. xe' y = 2(e +x'e)29. (2x sin y cos y)y' 4x +sin' y30. (x +e)y' = xe – 117. y = (4x + y)?19. xy' + 2ry 5y21. y' = y + y23. xy' + 6y = 3xyt/31. (x + y)y = x - y3. xy = y +2xy5. x(x+ y)y' = y(x – y) 6. (x + 2y)y' y7. xy'y' = x + y9. x'y = xy + y11. (x² – y?)y = 2ry12. xyy' = y? + x/4x? + y?13. xy = y +Vr + y?14. yy +x = x² + y?2. 2xyy' = x? + 2y?4. (x - y)y' = x+ y%3D8. x'y' = xy + x'erla10. xyy' = x? +3y?1.6 Substitution Methods and Exact Equations 73In Problems 31 through 42, verify that the given differentialequation is exact; then solve it.60. Use the method in Problem 59 to solve the differentialequationdy2y-x +731. (2x + 3y) dx + (3x +2y) dy = 032. (4x - y) dx + (6y – x) dy = 033. (3x? +2y?) dx+ (4xy +6y?) dy = 034. (2xy + 3x?) dx + (2x'y+4y) dy = 035. (x' +2) dx + (y² + In x) dy = 0dx 4x – 3y – 1861. Make an appropriate substitution to find a solution of theequation dy/dx = sin(x – y). Does this general solutioncontain the linear solution y(x) = x - 1/2 that is readilyverified by substitution in the differential equation?62. Show that the solution curves of the differential equation36. (1 + ye&#34;) dx + (2y + xe) dy = 0y(2r - y)x(2y3 - x)37. (cos x + In y) dx +dy = 0dydx

Accepted Answer

To solve given differential equation first we write it of the form of Bernoulli and solve it.

25. y (xy + y)(1 +x)/2=