Solve the differential equation. 5\sqrt{xy}\frac{dy}{dx}=1, x, y>0

Cem Hayes 2021-09-18 Answered
Solve the differential equation.
5xydydx=1,x,y>0
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Expert Answer

StrycharzT
Answered 2021-09-19 Author has 102 answers
Step 1
Given,
5xydydx=1,x,y>0
Step 2
Rewriting the equation,
5ydy=1xdx
Step 3
Integrate both sides,
5ydy=1xdx+C, C is constant.
5(y12+112+1)=(x12+112+1)+C
5(2y323)=2x12+C
y32=310(2x12+C)
y=(310(2x12+C))23
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