Can someone please help me solve these problems .21 and 33. 32. (x² + 2y²) dx = xy dy, y(-1) = 1dy33, 2x2- 3xy + y², y(1) = -2dx34. xy dx - x² dy = yVx² + y² dy,35. (x + ye/x) dx - xe/* dy = 0,X- (y cos - - x) dycos-x dy = 0,36. y dx +y(1) = 0y(0) = 237. (y² + 3xy) dx = (4x² + xy)dy,y(1) = 138. y³ dx = 2x³ dy – 2x²y dx, y(1) = √₂39. (x + √xy)=dydxdy ydxX44.40. y dx + x (lnx - In y - 1) dy = 0, y(1) = e41. y² dx + (x² + xy + y²) dy = 0, y(0) = 142. (√x + √y)² dx = x dy, y(1) = 0dy43. (x + √y² - xy).dx+ x - y = x-¹1/²y³/2, y(1) = 1y(0) = 1cosh= y, y(¹) = 1yy(1) = 0X45. Suppose M(x, y) dx + N(x, y) dy = 0 is a homogeneous equaticthat the substitution x = vy reduces the equation to one with sevariables.46. Suppose M(x, y) dx + N(x, y) dy = 0 is a homogeneous equatiothat the substitutions x = r cos 0, y = r sin 0 reduce the equatiowith separable variables.47. Suppose M(x, y)dx + N(x, y) dy = 0 is a homogeneous equationthat the equation has the alternative form dy/dxG(x/y.)48. If f(x,y) is a homogeneous function of degree n, show thataf= In Problems 11-30 solve the given differential equation by using anappropriate substitution.M.(x - y) dx + x dy = 0013) x dx + (y - 2x) dy = 0(15) (y² + yx) dx = x² dy = 0y - xdy17. =dxy + x19. -y dx + (x + √xy)dy = 021.) 2x2y dx = (3x³ + y³) dydydx X23.25. y=dxdyy+201Xyу2MOITAUOpups 021= x + 4ye27. y + x cot(x +e-2x/y117) d31. xy² dydxbittindx - x dy = 012. (x + y) dx + x dy = 014. y dx = 2(x + y) dy16. (y² + yx) dx + x² dy = 0dy x + 3y3x + y18. =dxdy20. x - y = √x² + y²dx22. (x4 + y4) dx - 2x³y dy = 0dy yx²dxX= y³ - x³, y(1) = 224.28.29. (x² + xy - y²) dx + xy dy = 030. (x² + xy + 3y2) dx = (x² + 2xy) dy = 0-=dydx X+26. (x²e-v/x + y²) dx = xy dyis any²= In+1XIn Problems 31-44 solve the given differential equation subject to theindicated initial condition.

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There are mentioned two question according to our guidelines i solving first one (question 21)…

2x²y dx = (3x³ + y³) dy du