Homework SourseHow do I integrate this ODE dxdt kx2n Fn where Force and k
How do I integrate this ODE
dx/dt = -kx^2/n = F/n where Force and k and n are constants.
Normally if its x instead of x^2, I know the integrating factor would be e^-(k/n)t but the x^2 is throwing me off. Thank you.
dx/dt = -kx^2/n = F/n where Force and k and n are constants.
Normally if its x instead of x^2, I know the integrating factor would be e^-(k/n)t but the x^2 is throwing me off. Thank you.
Solution
dx/dt = (F+kx2)/n
=> dx /F+kx2 = dt/n
=> kdx / (F/K)2 + x2 = dt/n
=> K* 1/ (F/K)* tan-1(x*K/F) = C* t/n where C is the integration constant
=> (k/F)*tan-1(x*K/F) = C*t/n
