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nevsk [136]
3 years ago
12

Giải các phương trình vi phân sau y' - y/x+1 = 2

Mathematics
1 answer:
KatRina [158]3 years ago
3 0

It looks like the differential equation is

y'-\dfrac y{x+1}=2

Multiply both sides by 1/(<em>x</em> + 1) :

\dfrac{y'}{x+1}-\dfrac y{(x+1)^2} = \dfrac2{x+1}

The left side is now a derivative of a product,

\left(\dfrac y{x+1}\right)' = \dfrac2{x+1}

Integrate both sides with respect to <em>x</em> :

\dfrac y{x+1} = 2\ln|x+1|+C

Solve for <em>y</em> :

y = 2(x+1)\ln|x+1| + C(x+1)

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