Rice: Created page with "Category:Differential Equations The '''reduction of order''' technique allows one to find a second solution to a differential equation when one solution is already found. Take a linear second order constant coefficient homogeneous ODE (see Second order linear ODE) with one repeated-root solution. Add u(t) as follows $y(t)=u(t)e^{2t}$ Substituting into the ODE, and you get $u'' = 0$ Integrating up, and you get u in the form $..."$

2024-05-22T05:09:50Z

Created page with "Category:Differential Equations The '''reduction of order''' technique allows one to find a second solution to a differential equation when one solution is already found. Take a linear second order constant coefficient homogeneous ODE (see Second order linear ODE) with one repeated-root solution. Add u(t) as follows <math> y(t)=u(t)e^{2t} </math> Substituting into the ODE, and you get <math> u'' = 0 </math> Integrating up, and you get u in the form <math>..."

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[[Category:Differential Equations]]
The '''reduction of order''' technique allows one to find a second solution to a differential equation when one solution is already found.

Take a linear second order constant coefficient homogeneous ODE (see [[Second order linear ODE]]) with one repeated-root solution. Add u(t) as follows

<math>
y(t)=u(t)e^{2t}
</math>

Substituting into the ODE, and you get

<math>
u'' = 0
</math>

Integrating up, and you get u in the form

<math>
u=te^{2t}
</math>

Reduction of order - Revision history