Solve the given differential equation subject to the specified initial condition. $\frac { d y } { d t } = \frac { \cos t } { 9 y } ; y ( 0 ) = 3$
A) $y ( t ) = 3 - \sqrt { \frac { 2 } { 9 } \sin t }$
B) $y ( t ) = 3 + \sqrt { \frac { 2 } { 9 } \sin t }$
C) $y ( t ) = \sqrt { \frac { 2 } { 9 } \sin t + 9 }$
D) $y ( t ) = \sqrt { 9 - \frac { 2 } { 9 } \sin t }$

Question

Quizplus · Accepted Answer

To solve the differential equation $\frac { d y } { d t } = \frac { \cos t } { 9 y }$, we separate variables and integrate both sides. This gives us $\int 9y dy = \int \cos t dt$, leading to $\frac{9y^2}{2} = \sin t + C$. Using the initial condition $y(0) = 3$, we find $C = \frac{81}{2}$. Solving for $y(t)$, we get $y(t) = \sqrt{\frac{2}{9}\sin t + 9}$.

Solve the Given Differential Equation Subject to the Specified Initial dydt=cos⁡t9y;y(0)=3\frac { d y } { d t } = \frac { \cos t } { 9 y } ; y ( 0 ) = 3dtdy​=9ycost​;y(0)=3

Solve the Given Differential Equation Subject to the Specified Initial $\frac { d y } { d t } = \frac { \cos t } { 9 y } ; y ( 0 ) = 3$