2 years ago

Add and subtract function PLS HELP!!!!

Mathematics

1 answer:

Fittoniya [83]2 years ago

4 0

Answer:

The first option:

$6x^{2} -4x+6$

Step-by-step explanation:

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Solve the differential equation.<br><br> dp/dt = t^2p - p + t^2 - 1

Alborosie

$\frac{dp}{dt} = t^2 p - p + t^2 - 1 \Rightarrow \frac{dp}{dt} = p(t^2 - 1)+ 1(t^2 - 1 ) \Rightarrow \\
\\
\frac{dp}{dt} = (p+1)(t^2 - 1)\ \Rightarrow\ \frac{dp}{p+1} = \left(t^2 - 1\right)dt\ \Rightarrow \\ \\
\int \frac{dp}{p+1} =\int \left(t^2 - 1\right)dt\ \Rightarrow \ \ln|p+1| = \frac{1}{3}t^2 - t + C \ \Rightarrow \\ \\
|p+1| = e^{t^3/3 - t + C}\ \Rightarrow\ p+1 = \pm e^Ce^{t^3/3 - t} \Rightarrow \\ \\
p = Ke^{t^3/3 -t} - 1,\ \text{where $K = \pm e^C$}
$

Since $p = -1$ is also a solution, $K$ can equal 0, and hence, $K$ can be any real number.

7 0

3 years ago

1-(1/3) x 1-(1/3) x 1/3

PolarNik [594]

The solution is -4/9x + 1