given dy/dx=y cosx, find the general solution given that y=2 when x= π /6

[markosheehan]

given the differential equation dy/dx=y cosx
find the general solution given that y=2 when x= π /6
i cant solve this
i tried integration

but then i get ln(2)=sinx+c and then when i put in 2 for y and π /6 for x i get ln(2)=1/2 + c and this is not the answer the answer is y=2e^sinx-0.5

 

[Deleted member 4993]

given the differential equation dy/dx=y cosx
find the general solution given that y=2 when x= π /6
i cant solve this
i tried integration

but then i get ln(y)=sinx+c and then when i put in 2 for y and π /6 for x i get ln(2)=1/2 + c and this is not the answer the answer is y=2e^(sinx-0.5)

\(\displaystyle \displaystyle{\dfrac{dy}{dx} = y \ * \cos(x)}\)

\(\displaystyle \displaystyle{\dfrac{dy}{y} = \cos(x) dx}\)

\(\displaystyle \displaystyle{ln(y) = \sin(x) \ + \ C}\)

Using bdy condition

ln(2) = sin(π/6) + C → C = ln(2) - 1/2

so

ln(y) - ln(2) = sin(x) - 1/2 → ln(y/2) = sin(x) - 0.5

y/2 = e^[sin(x) - 0.5]

...... continue.....