Solve the initial value problem.
-$$\frac { d y } { d x } = \frac { 1 } { 2 \sqrt { x } } + 7 , y ( 4 ) = - 5$$
A) $y = \sqrt { x } + 7 x - 35$
B) $y = \frac { 1 } { \sqrt { x } } + 7 x - \frac { 67 } { 2 }$
C) $y = \sqrt { x } + 7 x + 25$
D) $y = \frac { - 1 } { 4 } \sqrt { x } + 7 x - \frac { 65 } { 2 }$

Question

Quizplus · Accepted Answer

Integrating the given differential equation $\frac { d y } { d x } = \frac { 1 } { 2 \sqrt { x } } + 7$ gives $y = \sqrt{x} + 7x + C$. Using the initial condition $y(4) = -5$, we find $C = -35$, so the solution is $y = \sqrt { x } + 7 x - 35$.

Solve the Initial Value Problem dydx=12x+7,y(4)=−5\frac { d y } { d x } = \frac { 1 } { 2 \sqrt { x } } + 7 , y ( 4 ) = - 5dxdy​=2x​1​+7,y(4)=−5

Solve the Initial Value Problem $\frac { d y } { d x } = \frac { 1 } { 2 \sqrt { x } } + 7 , y ( 4 ) = - 5$