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Solve the initial value problem: `dy/dt = sint+1` , `y(pi/3) = 1/2` I do not know how...
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High School Teacher
`dy/dt=sint + 1`
To solve, isolate dy.
Then, integrate both sides.
`int dy =int(sint+1)dt`
`int dy= int sint dt + int 1dt`
To integrate, apply the formulas `int du=u +C` and `int sinudu=-cosu +C` .
`y+C=-cost +C+t +C`
Since C represents any number (constant), we may re-write the equation with one C only.
`y=-cost + t+C`
To get the value of C, use the condition y(pi/3)=1/2. So, plug-in t=pi/3 and y=1/2.
Then, isolate C.
And, plug-in the value of C to `y=-cost +t + C` .
Hence, the equation is:
`y=-cost +t + 1-pi/3`
Posted by mjripalda on November 16, 2013 at 1:48 AM (Answer #1)
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