Homework SourseThe functions y x2 cx2 are all solutions of equation xy 2y
The functions
y = x2 + c/x^2
are all solutions of equation:
xy?+ 2y = 4x2, (x > 0).
Find the constant c which produces a solution which also satisfies the initial condition y(6) = 7.
y = x2 + c/x^2
are all solutions of equation:
xy?+ 2y = 4x2, (x > 0).
Find the constant c which produces a solution which also satisfies the initial condition y(6) = 7.
Solution
The functions
y = x2 + c/x^2
are all solutions of equation:
xy+ 2y = 4x2, (x > 0).
y\' = 2x - 2C/x^3
xy\' + 2y = x (2x- 2C/x^3) +2 (x^2+ C/x^2) = 2x^2 - 2c/x^2 + 2x^2 + 2c/x^2 = 4x^2
which satisifies.
Find the constant c which produces a solution which also satisfies the initial condition y(6) = 7.
7 = 6^2 + C/ 6^2
7 - 36 = C/6^2
C = -29*36 = -1044
