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If y is a function of x then (d 2 y/dx 2) + y.(dy/dx) = 0. If x is a function of y , then what does the same differential equation become ?

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 ?

Grade:Upto college level

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
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,
askIITians Faculty
Ph.D,IIT Delhi

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