Find the general solution for the differential equation. $$ y \frac{d y}{d x}=x^{2}-7 x $$ A. $$ y=\frac{2}{3} x^{3}-7 x^{2}+C $$ B. $$ y=\frac{1}{3} x^{3}-7 x+C $$ C. $$ y^{2}=\frac{1}{3} x^{3}-7 x^{2}+C $$ D. $$ y^{2}=\frac{2}{3} x^{3}-7 x^{2}+C $$

Question

Gough Christensen · Accepted Answer

The general solution for the differential equation is $$ y^2 = \frac{2}{3} x^3 - 7x^2 + C $$, which matches option D.

Find the general solution for the differential equation. \( y \frac{d y}{d x}=x^{2}-7 x \) A. \( y=\frac{2}{3} x^{3}-7 x^{2}+C \) B. \( y=\frac{1}{3} x^{3}-7 x+C \) C. \( y^{2}=\frac{1}{3} x^{3}-7 x^{2}+C \) D. \( y^{2}=\frac{2}{3} x^{3}-7 x^{2}+C \)

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Find the general solution for the differential equation. \( y \frac{d y}{d x}=x^{2}-7 x \) A. \( y=\frac{2}{3} x^{3}-7 x^{2}+C \) B. \( y=\frac{1}{3} x^{3}-7 x+C \) C. \( y^{2}=\frac{1}{3} x^{3}-7 x^{2}+C \) D. \( y^{2}=\frac{2}{3} x^{3}-7 x^{2}+C \)

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Solución paso a paso

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