# 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 ?

Sumit Majumdar IIT Delhi
8 years ago
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,