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If y is a function of x then  (d2y/dx2) + y.(dy/dx) = 0.  If x is a function of y , then what does the same differential equation become ?

3 years ago

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Solution:
Let us assume a solution of the original differential equation as:
$y=e^{ax}$
Hence the given differential equation becomes:
$a^{2}e^{ax}+ae^{2ax}=0 \Rightarrow e^{ax}=-a \Rightarrow y=\frac{logy}{x} \Rightarrow y^{1/y}=e^{x}$

Thanks & Regards

Sumit Majumdar,

Ph.D,IIT Delhi

one year ago

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