<p>can anyone help me find a nice, elegant solution to this problem:
Show that y" - 2ay' + (a^2+b^2)y = 0 if y = (e^(ax))sinbx</p>
<p>every time I try it, I use like three sheets of paper and get nowhere. any tips would be really appreciated. :)</p>
<p>the above is true for all real x.</p>
<p>find y', and do not try to simplify</p>
<p>find y'', simplify the a^2 -b^2 part, and the 2ab part.</p>
<p>put them back into original equation and you should find everything cancels out nicely.</p>
<p>i agree... just find each derivative and sub it in.</p>