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Solving Differential Equations

57. Show that the substitution v = lny transforms the differential equation
dy/dx + P(x)y = Q(x)(ylny) into the linear equation dv/dx + P(x) = Q(x)v(x)

58. Use the idea in Problem 57 to solve the equation
x (dy/dx) - 4x2y + 2ylny = 0

59. Solve the differential equation dy/dx = (x-y-1)/(x+y+3) by finding h and k so that the substitutions x = u + h, y = v + k transform it into the homogeneous equation
dv/du = (u - v)/ (u + v)

60. Use the method in Problem 59 to solve the differential equation
dy/dx = (2y - x + 7) / (4x - 3y - 18)

keywords: ODE, ODEs

Solution Summary

Differential equations are solved. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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