Nope. That condition y(-4) = e should have tipped you off that logs/exponentials were involved.
dy/dx = 4y/x^2
dy/y = 4/x^2
lny = -4/x + c
y = c*e^(-4x)
note that the two c values are different. We could have said that
lny = -4/x + lnc
y = e^(-4/x + lnc)
= e^(-4/x)*e^(lnc)
= c*e^(-4/x)
Now, y(-4) = e, so
ce^(-4/-4) = e
ce^1 = e
c = 1
y = e^(-4/x)
Did you check your answer?
y = -1 - 4/x
y' = 4/x^2
But you wanted y' = 4y/x^2
checking my answer,
y' = (4/x^2) e^(-4/x) = 4y/x^2
Find the specific solution of the differential equation dy/dx = 4y/x^2 with condition y(−4) = e.
y= -1 - 4/x <- my answer
y=-1*e^(1/x)
y=e^(-4/x)
None of these
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1 answer