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CaHeK987 [17]
2 years ago
13

Please help , giving brainliest .. and a thanks !!

Mathematics
1 answer:
astraxan [27]2 years ago
3 0

Answer:

B, D, E

Step-by-step explanation:

yes

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Find the solution of the initial value problem<br><br> dy/dx=(-2x+y)^2-7 ,y(0)=0
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Substitute v(x)=-2x+y(x), so that \dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}. Then the ODE is equivalent to

\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7

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\dfrac{\mathrm dv}{v^2-9}=\mathrm dx

Split the left side into partial fractions,

\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)

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\dfrac6{v+3}=1-Ce^{6x}

v=\dfrac6{1-Ce^{6x}}-3

-2x+y=\dfrac6{1-Ce^{6x}}-3

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Given the initial condition y(0)=0, we find

0=\dfrac6{1-C}-3\implies C=-1

so that the ODE has the particular solution,

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