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faust18 [17]
3 years ago
12

Solve the differential equation dy/dx=2*y/x,x>0 simplify?

Mathematics
1 answer:
Andrew [12]3 years ago
4 0
Separate your variables:

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2y}x\implies \dfrac{\mathrm dy}y=2\dfrac{\mathrm dx}x

Integrating both sides gives

\displaystyle\int\frac{\mathrm dy}y=2\int\frac{\mathrm dx}x\implies \ln|y|=2\ln|x|+C\implies y=e^{2\ln|x|+C}=Cx^2
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