For the differential equation, find the particular solution if $y ( 5 ) = \frac { 1 } { 5 }$ . $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x y ^ { 2 } } { x ^ { 2 } + 8 }$
A) $y = - \ln \left( x ^ { 2 } + 8 \right) - 5 - \frac { \ln 33 } { 2 }$
B) $y = - \ln \left( x ^ { 2 } - 8 \right) - 5 - \frac { \ln 33 } { 2 }$
C) $y = \frac { 2 } { \ln \left( 2 x ^ { 2 } + 8 \right) - 5 - \ln 33 }$
D) $y = - \frac { 2 } { \ln \left( x ^ { 2 } + 8 \right) - 5 }$
E) $y = - \frac { 2 } { \ln \left( x ^ { 2 } + 8 \right) - 10 - \ln 33 }$

Question

For the differential equation, find the particular solution if $y ( 5 ) = \frac { 1 } { 5 }$ .   $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x y ^ { 2 } } { x ^ { 2 } + 8 }$  
A) $y = - \ln \left( x ^ { 2 } + 8 \right) - 5 - \frac { \ln 33 } { 2 }$
B)   $y = - \ln \left( x ^ { 2 } - 8 \right) - 5 - \frac { \ln 33 } { 2 }$
C)   $y = \frac { 2 } { \ln \left( 2 x ^ { 2 } + 8 \right) - 5 - \ln 33 }$
D)   $y = - \frac { 2 } { \ln \left( x ^ { 2 } + 8 \right) - 5 }$
E)   $y = - \frac { 2 } { \ln \left( x ^ { 2 } + 8 \right) - 10 - \ln 33 }$

Quizplus · Accepted Answer

The Answer of For the differential equation, find the particular solution if $y ( 5 ) = \frac { 1 } { 5 }$ .   $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { x y ^ { 2 } } { x ^ { 2 } + 8 }$  
A) $y = - \ln \left( x ^ { 2 } + 8 \right) - 5 - \frac { \ln 33 } { 2 }$
B)   $y = - \ln \left( x ^ { 2 } - 8 \right) - 5 - \frac { \ln 33 } { 2 }$
C)   $y = \frac { 2 } { \ln \left( 2 x ^ { 2 } + 8 \right) - 5 - \ln 33 }$
D)   $y = - \frac { 2 } { \ln \left( x ^ { 2 } + 8 \right) - 5 }$
E)   $y = - \frac { 2 } { \ln \left( x ^ { 2 } + 8 \right) - 10 - \ln 33 }$

For the Differential Equation, Find the Particular Solution If y(5)=15y ( 5 ) = \frac { 1 } { 5 }y(5)=51​

For the Differential Equation, Find the Particular Solution If $y ( 5 ) = \frac { 1 } { 5 }$