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explaining what i did to try and figure the problem out
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pyat
pyat
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I'm having a lot of trouble with this particular differential equation, mainly because I don't think I've ever done a nonlinear second order ODE. But here's the equation:

$$y''(t)+2\beta [y'(t)]^2+c^2 y(t)=0 \quad \text{where $\beta$ and $c^2$ are constants}$$ $$\text{initial conditions:}\quad y(0)=0, \quad y'(0)=v_0$$

My first thought was to do a Laplace Transform, but I'm pretty sure those only work on linear differential equations, so I'm not sure how to proceed..

Like I'm just genuinely stuck on how to even start. If possible it would be preferable to find an analytical solution. Any help is appreciated, thanks in advance.

I'm having a lot of trouble with this particular differential equation, mainly because I don't think I've ever done a nonlinear second order ODE. But here's the equation:

$$y''(t)+2\beta [y'(t)]^2+c^2 y(t)=0 \quad \text{where $\beta$ and $c^2$ are constants}$$ $$\text{initial conditions:}\quad y(0)=0, \quad y'(0)=v_0$$

Like I'm just genuinely stuck on how to even start. If possible it would be preferable to find an analytical solution. Any help is appreciated, thanks in advance.

I'm having a lot of trouble with this particular differential equation, mainly because I don't think I've ever done a nonlinear second order ODE. But here's the equation:

$$y''(t)+2\beta [y'(t)]^2+c^2 y(t)=0 \quad \text{where $\beta$ and $c^2$ are constants}$$ $$\text{initial conditions:}\quad y(0)=0, \quad y'(0)=v_0$$

My first thought was to do a Laplace Transform, but I'm pretty sure those only work on linear differential equations, so I'm not sure how to proceed..

Like I'm just genuinely stuck on how to even start. If possible it would be preferable to find an analytical solution. Any help is appreciated, thanks in advance.

Source Link
pyat
pyat
  • 69
  • 6

solving this second order nonlinear differential equation

I'm having a lot of trouble with this particular differential equation, mainly because I don't think I've ever done a nonlinear second order ODE. But here's the equation:

$$y''(t)+2\beta [y'(t)]^2+c^2 y(t)=0 \quad \text{where $\beta$ and $c^2$ are constants}$$ $$\text{initial conditions:}\quad y(0)=0, \quad y'(0)=v_0$$

Like I'm just genuinely stuck on how to even start. If possible it would be preferable to find an analytical solution. Any help is appreciated, thanks in advance.