Question

Which of the following is the solution to the differential equation....

Answer 1

B

Explanation:

`(dy)/(dx)= (x-2)(y-2)\\ y>2\\(dy)/(y-2)=(x-2)dx\\`

integrate both side

∫
`(dy)/(y-2)=`∫
`(x-2)dx\\`

`ln(y-2)=((x-2)^2)/(2) +C\\`

Substitute y(4)=5

`ln3=2+C\\C=ln3-2`

`ln(y-2)=((x-2)^2)/(2) +ln(3)-2\\y-2=e^{((x-2)^2)/(2) +ln(3)-2}\\y=2+3e^{(x^2)/(2)-2x }`