What is the slope.........................

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Ответ:

tyhe

15.05.2023

Mathematics

You're given the general solution,

y=C_1e^x+C_2xe^x+C_3x^2e^x

Use the given initial values to find C_1,C_2,C_3 :

$y(0)=2\implies2=C_1$

y'=C_1e^x+C_2(1+x)e^x+C_3(2x+x^2)e^x

$y'(0)=0\implies0=C_1+C_2$

$\implies C_2=-2$

y''=C_1e^x+C_2(2+x)e^x+C_3(2+4x+x^2)e^x

$y''(0)=0\implies0=C_1+2C_2+2C_3$

$\implies C_3=1$

Then the particular solution is

y=2e^x-2xe^x+x^2e^x

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