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Non linear second order differential equation

  1. Aug 6, 2012 #1
    I tried to find the non linear second order differential solution of:
    diff(y(t), t, t)-(diff(y(t), t))+exp(y(t)) = 0
    can any one please help me?

    Kind regards,
  2. jcsd
  3. Aug 6, 2012 #2


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    Science Advisor

    What do "diff(y(t), t, t)" and "diff(y(t), t)" mean? Second and first derivatives? I would think the usual "d^2y/dt^2" and "dy/dt" would be simpler. If this is y''- y'= e^y then, since the independent variable, t, does not appear explicitely, we can use "quadrature". Let z= dy/dt so that d^2y/dt^2= dz/dt= (dz/dy)(dy/dt)= z dz/dy. Then the equation becomes dz/dy- z= e^y, a linear first order differential equation. Solve for z as a function of y then solve dy/dt= z for y as a funtion of t.
  4. Aug 6, 2012 #3
    Thankyou for the reply. However in your explanation you have said d^2y/dt^2= dz/dt= (dz/dy)(dy/dt)= z dz/dy.if i understood it correctly,the equation becomes z*dz/dy- z= e^y, not " dz/dy- z= e^y,". hence it will not be linear first order equation.

    Thank you in advance.
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