GATE 2021 MA – Question 30
For x²y″−4xy′+6y=0,x>0, with y(2)=0,y′(2)=4, find y(4).
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Correct answer: 32 to 32
Explanation
The Euler equation has exponents r(r−1)−4r+6=(r−2)(r−3)=0. Thus y=Cx²+Dx³. Conditions give 4C+8D=0 and 4C+12D=4, so D=1,C=−2. Then y(4)=−32+64=**32**.