Hello!(adsbygoogle = window.adsbygoogle || []).push({});

On Pauls notes webpage, there is the following problem to be solved by variation of parameters:

[itex]ty''-(t+1)y'+y=t^2[/itex] (1)

On the page, the fundamental set of solutions if formed on the basis of the complementary solution. The set is:

[itex]y_{1}(t)=e^t[/itex] and [itex]y_{2}(t)=t+1[/itex]

Now, I must be missing something here. Since I get the complementary solution for the homogeneous equation of (1):

[itex]r=\frac{(t+1)+/- \sqrt{(t+1)^2-4t}}{2t}[/itex] which solves as [itex]r_{1}=1[/itex] and [itex]r_{2}=\frac{1}{t}[/itex] which would give a complementary solution of:

[itex]Y_{c}=C_{1}e^{t}+C_{2}e^{\frac{1}{t}t}=C_{1}e^{t}+C_{2}e^1[/itex]

from which I would get [itex]y_{1}(t)=e^t[/itex] and [itex]y_{2}(t)=e[/itex]

What have I missed, must be simple...

Regards,

U.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Problem with finding the complementary solution of ODE

Loading...

Similar Threads - Problem finding complementary | Date |
---|---|

A Solving an ODE Eigenvalue Problem via the Ritz method | Mar 14, 2018 |

Problem with finding an Inverse Laplace Transform | Jul 16, 2011 |

Problem in finding relationship of ordinary differential equ | Jan 15, 2011 |

Where ı can find problems about first order diff. equations | Jun 14, 2007 |

**Physics Forums - The Fusion of Science and Community**