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Math Help - differential equations

  1. #1
    Junior Member
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    differential equations

    i need help with some of these, i kind of know how to do it, but i get stuck...

    1. dy/dx = (ycosx)/(1+y^2) y(0)=1
    i know how to get to the integral of both sides what to i do becuase i get a y^2 on the left?
    we are supposed to solve the equation using the values given..

    2. dz/dt + e^(t+z)

    im not sure how to separate the equations here

    3. dp/dt = sqrt(pt) p(1) = 2
    im not sure if i got this right but i got p = sqrt (1/4sqrt(t) + 15/4)

    please help!! thankss!
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  2. #2
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    \frac{dy}{dx} = \frac{y\cos{x}}{1+y^2}<br />

    \frac{1+y^2}{y} \, dy = \cos{x} \, dx

    \int \frac{1}{y} + y \, dy = \int \cos{x} \, dx



    \frac{dz}{dt} = e^{t+z}

    \frac{dz}{dt} = e^t \cdot e^z

    \int e^{-z} \, dz = \int e^t \, dt



    \frac{dp}{\sqrt{p}} = \sqrt{t} \, dt

    2p^{\frac{1}{2}} = \frac{2}{3} t^{\frac{3}{2}} + C

    p^{\frac{1}{2}} = \frac{1}{3} t^{\frac{3}{2}} + C

    p = \left(\frac{1}{3} t^{\frac{3}{2}} + C\right)^2
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