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38 votes
38 votes
10yy'=x y(10)=4

Find the solution of the differential equation that satisfies the given initial condition.

User Schien
by
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1 Answer

6 votes
6 votes

Answer:

Explanation:

10yy'=x


10y(dy)/(dx) =x\\separating~the~variables\\10 ydy=xdx\\integrating\\\int 10ydy=\int xdx+c\\(10y^2)/(2) =(x^2)/(2) +c\\10y^2=x^2+2c\\when~x=10\\y=4\\10(4)^2=10^2+2c\\160=100+2c\\2c=160-100=60\\c=(60)/(2) =30\\10y^2=x^2+60\\10y^2-x^2=60

User Erich Kitzmueller
by
2.6k points
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