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LekaFEV [45]
4 years ago
5

Please show me how to solve the initial value problem y'=tanx y(pi/4)=3

Mathematics
1 answer:
AlexFokin [52]4 years ago
4 0
The ODE is separable, i.e. you can write

\dfrac{\mathrm dy}{\mathrm dx}=\tan x\iff\mathrm dy=\tan x\,\mathrm dx

Integrating both sides gives the general solution.

\displaystyle\int\mathrm dy=\int\tan x\,\mathrm dx
y=-\ln|\cos x|+C

Given that y\left(\dfrac\pi4\right)=3, we have

3=-\ln\left|\cos\dfrac\pi4\right|+C
3=-\ln\dfrac1{\sqrt2}+C
3-\ln\sqrt2=C


and so the particular solution to the IVP is

y=-\ln|\cos x|+3-\ln\sqrt2
y=3-\ln|\sqrt2\cos x|
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<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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Distributive Property

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Step-by-step explanation:

<u>Step 1: Define Systems</u>

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<u>Step 2: Rewrite Systems</u>

2x - y = 11

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<u>Step 3: Redefine Systems</u>

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  5. [Division Property of Equality] Divide 7 on both sides:                                  x = 4
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