3 years ago

Rewrite n square root x square m using rational expression

Mathematics

1 answer:

Anna35 [415]3 years ago

5 0

Step-by-step explanation:

$\sqrt[?]{?}$

x m

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$20 \frac{1}{2} :2 \frac{1}{4} = \frac{41}{2}: \frac{9}{4}= \frac{41}{2}* \frac{4}{9} =\frac{82}{9} = 9 \frac{1}{9} \ \ \text{miles per hour}$

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Step-by-step explanation:

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Slav-nsk [51]

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3 years ago

Find the general solution of the nonhomogeneous differential equation x^2y''-2y=3(x^2) -1, (x>0).

Ira Lisetskai [31]

Answer:

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Step-by-step explanation:

We are given that non-homogeneous differential equation

$x^2y''-2y=3(x^2)-1$

It is Cauchy Euler equation

Substitute x=e^t x>0

Auxillary equation

$D'(D'-1)-2=0$

$D'^2-D'-2=0$

$(D'-2)(D'+1)=0$

$D'-2=0 \implies D'=2$

$D'+1=0\implies D'=-1$

Complementary solution

$y=C_1e^{-t}+C_2e^{2t}$

$y=C_1\frac{1}{x}+C_2x^2$

Particular solution

$y_p=\frac{3e^{2t}}{D'^2-D'-2}-\frac{e^{0t}}{D'^2-D'-2}$

$y_p=te^{2t}+\frac{1}{2}=x^2logx+\frac{1}{2}$

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Hence, general solution G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

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4 years ago