Solve the differential equation. $3 y y ^ { t } = 7 x$
A) $7 x ^ { 2 } + 3 y ^ { 2 } = C$
B) $3 x ^ { 2 } + 7 y ^ { 2 } = C$
C) $3 x ^ { 2 } - 7 y ^ { 2 } = C$
D) $7 x ^ { 2 } - 3 y ^ { 2 } = C$
E) $7 x ^ { 2 } + 3 y ^ { 2 } = 10$

Question

Quizplus · Accepted Answer

Rewrite the equation as $$\frac{dy}{dx}=\frac{7}{3}\cdot\frac{1}{y}.$$ Then we can separate the variables and integrate both sides: $$\int y dy=\frac{7}{3}\int dx.$$ This gives us $$\frac{y^2}{2}=\frac{7}{3}x+C,$$ where $C$ is the arbitrary constant. Rearranging this equation, we get $$7x^2-3y^2=C.$$ Thus, the answer is D.

Solve the Differential Equation 3yyt=7x3 y y ^ { t } = 7 x3yyt=7x

Solve the Differential Equation $3 y y ^ { t } = 7 x$