the functions yx2cx2 are all solutions of equation xy2y 4x2

the functions y=x^2+(c/x^2) are all solutions of equation xy\'+2y= 4x^2, (x>0). Find the constant c which produces a solution which also satisfies the initial condition y(5)=1
c=?

Solution

y(5)= 1 means when x=5 y has a value of 1. substituting these values in y=x^2+(c/x^2) 1=5^2+c/5^2 1=25+ c/25 c = -24*25 = -600
the functions y=x^2+(c/x^2) are all solutions of equation xy\'+2y= 4x^2, (x>0). Find the constant c which produces a solution which also satisfies the initia

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