數學題...只要答案，不要step

y(x)=(4*e^(3x)+2)e^(-3x)

y is defined in the implicit function:
y + 3xy -12x + 72 = 0

y=(12x-72)/(1+3x)







SOLUTION:

dy/dx + 3y = 12 and y(0) = 6
Integrate both side with respect to x

∫(dy/dx )+dx3y∫dx=∫12dx

y+3xy = 12x + C
when y=0, x=6
0+3*6(0)=12(6)+C
C=-72

Hence y is defined in the implicit function:
y + 3xy -12x + 72 = 0




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y(x)=(4*e^(3x)+2)e^(-3x)