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Let y(x) be the solution of x dy - (y² - 4y) dx = 0 for x > 0 with y(1) = 2, and suppose the slope of the curve y = y(x) is never zero. Find the value of 10 y(sqrt(2)).
- 8
- 20
- 24
- 40
Correct answer: 8
Solution
Separating and integrating with partial fractions gives (y-4)/y = C x⁴; the initial condition fixes the curve so that y(sqrt2) = 0.8, hence 10 y(sqrt2) = 8.
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