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

We can rewrite the given differential equation as 
$$\frac{dy}{dx}=\frac{7x}{3y}$$
Now, we can separate the variables and integrate both sides to get rid of the derivative:
$$\frac{3}{7}y \, dy=x \, dx$$
Integrating both sides gives us
$$\frac{3}{14}y^2=\frac{1}{2}x^2+C$$
which can also be written as
$$7x^2-3y^2=C$$
Therefore, the correct choice is (D).

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

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