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Sloan [31]
3 years ago
9

3. (6 Points). Solve the initial value problem y'-y.cosx=0, y(pi/2)=2e

Mathematics
1 answer:
Stells [14]3 years ago
7 0

Answer:

y=2e^{sin(x)}

Step-by-step explanation:

Given equation can be  re written as

\frac{\mathrm{d} y}{\mathrm{d} x}-ycos(x)=0\\\frac{\mathrm{d} y}{\mathrm{d} x}=ycos(x)\\\\=> \frac{dy}{y}=cox(x)dx\\\\Integrating  \\ \int \frac{dy}{y}=\int cos(x)dx \\\\ln(y)=sin(x)+c............(i)

Now it is given that y(π/2) = 2e

Applying value in (i) we get

ln(2e) = sin(π/2) + c

=> ln(2) + ln(e) = 1+c

=> ln(2) + 1 = 1 + c

=> c = ln(2)

Thus equation (i) becomes

ln(y) = sin(x) + ln(2)

ln(y) - ln(2) = sin(x)

ln(y/2) = sin(x)

y= 2e^{sinx}

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