Solve the differential equation. $3 y y ^ { \prime } = 7 x$
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

Rearrange the equation as $\frac{dy}{dx}=\frac{7}{3}\cdot\frac{x}{y}$. Then, using separation of variables, we have $\int y\,dy = \int \frac{7}{3}x\,dx$, which gives $\frac{y^2}{2}=\frac{7}{6}x^2+C$. Solving for $y^2$ and multiplying both sides by 2 gives the answer in the form $7x^2-3y^2=C$. Therefore, the best choice is (D).

Solve the Differential Equation 3yy′=7x3 y y ^ { \prime } = 7 x3yy′=7x

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