Non linear second order differential equation

[jj231]

Hello,
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 anyone please help me?

Kind regards,
JJ

 

[HallsofIvy]

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.

 

[jj231]

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.