Find the Solution of the Initial-Value Problem $\frac { d y } { d t } = \frac { 2 t } { y ^ { 2 } + t ^ { 2 } y ^ { 2 } }$

question 59

Multiple Choice

Find the solution of the initial-value problem $\frac { d y } { d t } = \frac { 2 t } { y ^ { 2 } + t ^ { 2 } y ^ { 2 } }$ , $y ( 0 ) = 3$ .

• A) \(y = 3 \ln \left( 1 + t ^ { 2 } \right) + 3 C\)
• B) \(y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) + 3 C }\)
• C) \(y = 3 \ln \left( 1 + t ^ { 2 } \right) + 9\)
• D) \(y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) + 9 }\)
• E) \(y = 3 \ln \left( 1 + t ^ { 2 } \right) + 27\)
• F) \(y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) + 27 }\)
• G) \(y = 3 \ln \left( 1 + t ^ { 2 } \right)\)
• H) \(y = \sqrt [ 3 ] { 3 \ln \left( 1 + t ^ { 2 } \right) }\)

Understand the principles of infection control and prevention.

Identify the steps in the proper donning of sterile gloves to reduce infection risk.

Recognize the importance of hand hygiene and antisepsis in preventing healthcare-associated infections.

Describe the signs of health care-associated infections and strategies for monitoring and prevention.