Solve the differential equation.
-$$\frac { d y } { d x } = 6 x \sqrt { 9 - y ^ { 2 } }$$
A) $y = 3 \sin \left( 3 x ^ { 2 } + C \right)$
B) $y = 3 \sin ^ { - 1 } \left( 3 x ^ { 2 } + C \right)$
C) $y = \sin ^ { - 1 } \left( 3 x ^ { 2 } + C \right)$
D) $y = \sin \left( 3 x ^ { 2 } + C \right)$

Question

Quizplus · Accepted Answer

This differential equation can be solved by separation of variables. Rearranging, we get $\frac{dy}{\sqrt{9-y^2}} = 6x dx$. Integrating both sides, we use the substitution $y = 3\sin(u)$ for the left side, leading to $u = 3x^2 + C$. Thus, $y = 3\sin(3x^2 + C)$ is the solution.

Solve the Differential Equation dydx=6x9−y2\frac { d y } { d x } = 6 x \sqrt { 9 - y ^ { 2 } }dxdy​=6x9−y2​

Solve the Differential Equation $\frac { d y } { d x } = 6 x \sqrt { 9 - y ^ { 2 } }$