An ordinary differential equation is given below: (\frac{d y}{d x})(x \ln x)=y The solution for the above equation is (Note: {K} denotes a constant in the options)

GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

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An ordinary differential equation is given below:

(\;{d y}/{d x})(x \ln x)=y

The solution for the above equation is
(Note:

{K}

denotes a constant in the options)

Solution:

\;{d y}/{d x} x \ln x=y

⇒ \;\; ∫ \;{d y}/{y}=∫ \;{d x}/{x \ln x}

taking

\ln x=t

⇒ \;{1}/{x} d x=d t

⇒ ∫ \;{d y}/{y}=∫ \;{d t}/{t}

⇒\;\; \ln x=\ln t+\ln k

⇒ \;\; y=k t

⇒y=k\ln x

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