Spin Posted March 1, 2006 Share Posted March 1, 2006 if y_1 and y_2 are the answers of this equation: (d^4 y/dx^4) + 4 y = f(x) then what's y_2 - y_1? I used laplace Transform! Thanks in advance Link to comment Share on other sites More sharing options...
the tree Posted March 1, 2006 Share Posted March 1, 2006 Surely you meant [math]\frac{d^{4}y}{dx^4}4y[/math], not [math]\frac{d^{4}y}{dx^4}+4y[/math]?? And what do you mean by "awnsers" anyway? Link to comment Share on other sites More sharing options...
NeonBlack Posted March 1, 2006 Share Posted March 1, 2006 I wouldn't be so sure about that. And by answer, he probably means 'What is y?' Link to comment Share on other sites More sharing options...
the tree Posted March 1, 2006 Share Posted March 1, 2006 Well... [math]\frac{d^{4}y}{dx^4}4y=\frac{d^{3}y}{dx^3}4=\frac{d^{2}y}{dx^2}0=\frac{dy}{dx}0=0[/math] So I guess the OPs meaning was correct on that account (somehow), but not knowing the meaning of [math]f(x)[/math], I don't see anything that can be done with it. Link to comment Share on other sites More sharing options...
NeonBlack Posted March 1, 2006 Share Posted March 1, 2006 f(x) is just an arbitrary function of x. But since I don't know how to solve 4th order DE's I'm afraid I can't be of much more help. Link to comment Share on other sites More sharing options...
Tom Mattson Posted March 1, 2006 Share Posted March 1, 2006 if y_1 and y_2 are the answers of this equation:(d^4 y/dx^4) + 4 y = f(x) then what's y_2 - y_1? OK so your equation is of the form [imath]\mathcal{L}[y]=f(x)[/imath]' date=' where [imath']\mathcal{L}=\frac{d^4}{dx^4}+4[/imath]. Use the fact that [imath]\mathcal{L}[/imath] is linear to find [imath]\mathcal{L}[y_2-y_1][/imath]. You should find that the difference of two solutions to the inhomogeneous equation [imath]\mathcal{L}[y]=f(x)[/imath] is actually a solution to the homogeneous equation [imath]\mathcal{L}[y]=0[/imath]. So your answer will be independent of [imath]f(x)[/imath]. It will of course depend on 4 arbitrary constants of integration. I used laplace Transform! That will work, so continue with it. Link to comment Share on other sites More sharing options...
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