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Math Question solution needed

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kakar133

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please solve this question... using separation of variables

dy/dx=ylny y(0)=5,
 

kakar133 said:
please solve this question... using separation of variables

dy/dx=ylny y(0)=5,
Click to expand...

\[\dfrac{dy}{y \ln{y}}=dx \;\;\longrightarrow\;\;\displaystyle\int{\dfrac{dy}{y \ln{y}}}=\ln(\ln{y})=C+x\]

at x=0 : \[\ln(\ln{5})=C \;\;\longrightarrow\;\; y=5^{e^x}\]
 
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