Solve the initial value problem for y as a function of x.
-$$\sqrt { 49 - x ^ { 2 } } \frac { d y } { d x } = 1 , x

Question

Solve the initial value problem for y as a function of x.
-$$\sqrt { 49 - x ^ { 2 } } \frac { d y } { d x } = 1 , x < 7 , y ( 0 ) = 12$$
A) $y = \ln | \sec x + \tan x | + 12$
B) $y = \ln | \sec x + \tan x |$
C) $y = \sin ^ { - 1 } \frac { x } { 7 }$
D) $y = \sin ^ { - 1 } \frac { x } { 7 } + 12$

Quizplus · Accepted Answer

First, we can simplify the differential equation by dividing both sides by $\sqrt{49-x^2}$ to obtain $\frac{dy}{dx} = \frac{1}{\sqrt{49-x^2}}$. Integrating both sides with respect to $x$ yields $y = \sin^{-1} \frac{x}{7} + C$, where $C$ is a constant. Plugging in the initial condition $y(0) = 12$ gives $C = 12$. Thus the solution is $y = \sin^{-1} \frac{x}{7} + 12$.

Solve the Initial Value Problem for Y as a Function 49−x2dydx=1,x<7,y(0)=12\sqrt { 49 - x ^ { 2 } } \frac { d y } { d x } = 1 , x < 7 , y ( 0 ) = 1249−x2​dxdy​=1,x<7,y(0)=12

Solve the Initial Value Problem for Y as a Function $\sqrt { 49 - x ^ { 2 } } \frac { d y } { d x } = 1 , x < 7 , y ( 0 ) = 12$