Question

The differential equation y $\frac{dy}{dx}$ + x = k (k Ī R) represents

• A. Family of circles centered at y axis
• B. Family of circles centered at x axis
• C. Family of rectangular hyperbola's
• D. Family of parabola's whose axis is x-axis

Answer 1

Answer: (B)

Family of circles centered at x axis

Answer 2

y $\frac{dy}{dx}$ = (k – x)

y dy = (k – x) dx

Integrate both side

$\int_{}^{}{ydy}$ = $\int_{}^{}{(k - x)}$dx

$\frac{y^{2}}{2}$ = – $\frac{(k - x)^{2}}{2}$ + c

$\frac{(k - x)^{2}}{2} + \frac{y^{2}}{2}$ = c family of circle center is (k, 0)