Question

Find a function y of x such that 2yy′=x and y(2)=6

Answer 1

`y=\sqrt{(x^(2))/(2) +34}`

Explanation:

`2y\left( x\right) y^(\prime )\left( x\right) =x`

`\Longrightarrow \int 2y\left( x\right) y^(\prime )\left( x\right) dx=\int x\ dx`

`\Longrightarrow y^(2)\left( x\right) =(x^(2))/(2) +c\ \text{(c is a constant)}`

`y\left( 2\right) =6\Longleftrightarrow y^(2)\left( 2\right) =36`

`y^(2)\left( 2\right) =36\Longleftrightarrow (\left( 2\right)^(2) )/(2) +c=36\ \Longleftrightarrow c=34`

`\Longrightarrow y\left( x\right) =\pm\sqrt{(x^(2))/(2) +34}`