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dbhuggybearow6jng
18.02.2020 •
Mathematics
Consider the initial value problem y' + 2 3 y = 1 − t 2 , y(0) = y0. Find the value of y0 for which the solution touches, but does not cross, the t-axis. (A computer algebra system is recommended. Round your answer to three decimal places.)
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Ответ:
Step-by-step explanation:
Given,
Integrating factor=![e^{\int{\frac{2}{3} dt}}=e^{\frac{2}{3}t}](/tpl/images/0513/6461/863af.png)
Multiplying the integrating factor
Integrating both sides
Given,y(0)=y₀
y(t)=0
Again since this solution has slope zero when it is just touche the t-axis.
y'(t)=0
Therefore
Ответ: