Let us solve the separable differential equation
dxdy=xy151+x
which is equivalent to
y15dy=x1+xdx
It follows that
∫y15dy=∫x1+xdx=∫(x1+1)dx.
Therefore, 16y16=ln∣x∣+x+C.
Since y(1)=5, we get that 16516=1+C, ànd hence C=16516−1.
We conclude that the solution is
16y16=ln∣x∣+x+16516−1 or
y16=16ln∣x∣+16x+516−16
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