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 ?


2 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 & RegardsSumit Majumdar,askIITians FacultyPh.D,IIT Delhi

4 months ago

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