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Grade Upto college levelIntegral Calculus

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 ?

Raghu Surat SVNIT

14 Years agoGrade Upto college level

1 Answer

Sumit Majumdar

12 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,

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Ph.D,IIT Delhi

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