(1 + x^2) (dy/dx) = y with y(0) = 1 the answer i am getting is y = e^(arctan x) is this correct?? also for (dy/dt)(cos t) + y(sin t) = 1 with y(Pi/4) = sqrt(2) the answer i am getting is y = (cos t)(tan t) + (1/2)(sqrt(2)) is this correct?

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- Feb 4th 2009, 03:25 PMcrafty[SOLVED] differential equation verification 2
(1 + x^2) (dy/dx) = y with y(0) = 1 the answer i am getting is y = e^(arctan x) is this correct?? also for (dy/dt)(cos t) + y(sin t) = 1 with y(Pi/4) = sqrt(2) the answer i am getting is y = (cos t)(tan t) + (1/2)(sqrt(2)) is this correct?

- Feb 4th 2009, 04:14 PMgalactus
Yes, the first one is correct.

The second should be $\displaystyle y=Ccos(t)+sin(t)$

Using the initial condition, C=1.

Therefore, $\displaystyle y=cos(t)+sin(t)$