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schepotkina [342]
3 years ago
8

Find the specific solution of the differential equation dy/dx= 4y/x^2 with condition y(-4)=1

Mathematics
1 answer:
Rina8888 [55]3 years ago
7 0

This ODE is separable:

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4y}{x^2}\implies\dfrac{\mathrm dy}y=\dfrac4{x^2}\,\mathrm dx

Integrating both sides gives

\ln|y|=-\dfrac4x+C

Given the initial condition y(-4)=1 we find

\ln|1|=-\dfrac4{-4}+C\implies C=-1

so that the particular solution is

\ln|y|=-\dfrac4x-1

\implies y=e^{-(1+4/x)})

so the answer is D.

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