Question

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

Answer 1

Answer:

B

Step-by-step explanation:

$\frac{dy}{dx}= (x-2)(y-2)\\ y>2\\\frac{dy}{y-2}=(x-2)dx$

integrate both side

∫$\frac{dy}{y-2}=$∫$(x-2)dx$

$ln(y-2)=\frac{(x-2)^2}{2} +C$

Substitute y(4)=5

$ln3=2+C\\C=ln3-2$

$ln(y-2)=\frac{(x-2)^2}{2} +ln(3)-2\\y-2=e^{\frac{(x-2)^2}{2} +ln(3)-2}\\y=2+3e^{\frac{x^2}{2}-2x }$