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Arada [10]
3 years ago
9

A set of equations is given below:

Mathematics
1 answer:
TEA [102]3 years ago
6 0
The 3rd selection is appropriate.

.. 5b +1 = a = 3b +5
by the transitive property of equality,
.. 5b +1 = 3b +5
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4x^2 y+8xy'+y=x, y(1)= 9, y'(1)=25
jarptica [38.1K]

Answer with explanation:

\rightarrow 4x^2y+8x y'+y=x\\\\\rightarrow 8xy'+y(1+4x^2)=x\\\\\rightarrow y'+y\times\frac{1+4x^2}{8x}=\frac{1}{8}

--------------------------------------------------------Dividing both sides by 8 x

This Integration is of the form ⇒y'+p y=q,which is Linear differential equation.

Integrating Factor

 =e^{\int \frac{1+4x^2}{8x} dx}\\\\e^{\log x^{\frac{1}{8}+\frac{x^2}{2}}\\\\=x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}

Multiplying both sides by Integrating Factor  

x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}\times [y'+y\times\frac{1+4x^2}{8x}]=\frac{1}{8}\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}\\\\ \text{Integrating both sides}\\\\y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=\frac{1}{8}\int {x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}} \, dx \\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=\int {x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}} \, dx\\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=-[x^{\frac{9}{8}}]\times\frac{ \Gamma(0.5625, -x^2)}{(-x^2)^{\frac{9}{16}}}\\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=(-1)^{\frac{-1}{8}}[ \Gamma(0.5625, -x^2)]+C-----(1)

When , x=1, gives , y=9.

Evaluate the value of C and substitute in the equation 1.

6 0
3 years ago
Consider the proposition
ddd [48]

your answer is C

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6 0
3 years ago
Read 2 more answers
What is the sum of the first 4 terms of a geometric sequence that has a first term of 2 and a ratio (multiplier) of 8?
taurus [48]

\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad  \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=2\\ r=8\\ n=4 \end{cases} \\\\\\ S_4=2\left( \cfrac{1-8^4}{1-8} \right)\implies S_4=2\left( \cfrac{-4095}{-7} \right) \\\\\\ S_4=2(585)\implies S_4=1170

6 0
3 years ago
Complete the sentence.<br><br><br> 7 is 35% of ________
nataly862011 [7]
7 is 35% of x.

Thus, since 35% = 35/100,

35% of x is 7, so 35/100 * x = 7.

35x/100 = 7

35x=700

x = 20
7 is 35% of 20.


4 0
3 years ago
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If the period of a sinusoidal function is equal to 18 what is it’s period
Ainat [17]

The period is 18... it’s the change in x of one wavelength

4 0
3 years ago
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