Solve the differential equation.
-$$\frac { d y } { d x } = 9 \sqrt { x y }$$
A) $y = 3 x ^ { 3 / 2 } + C$
B) $y = \left( 3 x ^ { 3 / 2 } + C \right) ^ { 2 }$
C) $y = 3 x ^ { 3 } + x ^ { 3 / 2 } + C$
D) $y = 9 x ^ { 3 } + C$

Question

Quizplus · Accepted Answer

Separate the variables and integrate both sides:
$$ \frac { 1 } { \sqrt { y } } d y = 9 \sqrt { x } d x $$
$$ 2 \sqrt { y } = 3 x ^ { 3 / 2 } + C $$
Solving for $y$, we get
$$ y = \left( \frac { 3 } { 2 } x ^ { 3 / 2 } + \frac { C } { 2 } \right) ^ { 2 } $$
which matches option (B) with a different constant. Therefore, the answer is (B).

Solve the Differential Equation dydx=9xy\frac { d y } { d x } = 9 \sqrt { x y }dxdy​=9xy​

Solve the Differential Equation $\frac { d y } { d x } = 9 \sqrt { x y }$