Solve second order nonlinear differential equation

Alfredo1511

how do you solve this equation?

y´´ + k/(y^2) = 0 ? I got it from applying Newton's 2nd law of motion to an object falling from space to earth only affected by gravitational force. Thank you!

Related Classical Physics News on Phys.org

vanhees71

Gold Member
Is this a homework problem? If so, you should post it in the homework section. So I'll give only a hint to the solution:

You can find a first integral of the equation of motion, which is nothing than energy conservation, by multiplying with $\dot{y}$ (assuming that your prime means in fact a time derivative). Then you get a first-order equation, which can be solved by separation of variables.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving