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3 years ago

Find the coordinates of the point where y-4x=1 crosses the y axis

Mathematics

2 answers:

denpristay [2]3 years ago

7 0

Answer:

(a) (-1/4,0)

(b) k = (10-c)/2

Step-by-step explanation:

(a) A point passing through the y-axis is the same as finding the y-intercept.

[Move terms to right-hand side; y = mx + b form]

y = 4x + 1

[Find x, when y = 0]

0 = 4x + 1

-1 = 4x

-1/4 = x

At x = -1/4, y = 0 therefore the point: (-1/4,0) crosses the y-axis.

(b) To find the value of k in (k,10), we need to find x. Given y= 10 x=k c=constant

[Find x by plugging in known values]

Using y = 2x + c,

10 = 2k + c

10 - c = 2k

(10-c)/2 = k

hoa [83]3 years ago

7 0

Answer:

first one is -1,0

Step-by-step explanation:

i just did it

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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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