This ODE has characteristic equation
which has roots at 
. Then the characteristic solution to the ODE is
<span>We have 75 mL of 4% sugar solution.
We have to add a 30% sugar </span><span>solution to make a 50% </span><span>sugar solution.
75 * .04 + .30x = .50 * (75 +x)
3 + .30x = 37.5 +.50x
I can't get the equation to solve.
Did you type it correctly? For one thing, you have the percentages typed as .30 % and 4%. Are the decimal places in the correct positions?
Also, no matter how much 30% sugar solution you add, it will NEVER increase to 50%.
</span>
There are 4,000 Grams in 4 Kilograms
log(3x) = log(2x-4)
taking antilog of both sides:
3x = 2x - 4
3x - 2x = -4 [subtracting 2x from both sides]
x = -4
and we're done already!
