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 Differential Equations Ordinary and Partial Differential Equations Math Forum

November 14th, 2010, 08:19 PM   #11
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Re: Differential Equations

Quote:
 Originally Posted by MathematicallyObtuse $\text{(1 a)\,\,Solve the following}$ $(ii)\,\,100\frac{d^2r}{dt^2}\,-\,60\frac{dr}{dt}\,+\,9r\,=\,0$ $100\frac{d^2r}{dt^2}\,-\,60\frac{dr}{dt}\,+\,9\,=\,0$ $100u^2\,-\,60u\,+\,9\,=\,0$ $100u^2\,-\,30u\,-\,30u\,+\,9\,=\,0$ $(10u\,-\,3)^2\,=\,0$ $u\,=\,\frac{3}{10}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\alpha\,=\,\ beta\,=\,\frac{3}{10}$ $y\,=\,e^{\frac{3}{10}}\,(A\,+\,Bx)$
Maybe a typo happens....

$y\,=\,e^{\frac{3}{10}x}\,(A\,+\,Bx)$

Quote:
 Originally Posted by MathematicallyObtuse $(iii)\,\,\frac{d^2x}{dt^2}\,+\,x\,=\,10e^2t$ $u^2\,+\,1\,=\,0$ $u= \pm\,1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\,p = 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\ ,\,\,\,\,\,\,\,\,\,\,q = 1$ $x\,=\,A\,\cos t\,+\,B\,\sin t$ $x\,=\,C\,e^t\,+\,D$ $x^'\,=\,t\,Ce^t$ $x^''\,=\,t^2\,Ce^t$ $t^2\,Ce^t\,+\,Ce^t\,+\,D\,=\,10e^2t$ $e^t\,=\,10^2\,=\,C\,+\,t^2\,C$ $10^2\,=\,C(1\,+\,t^2)$ $y\,=\,A\,\cos t\,+\,B\,\sin t\,+\,\frac{100}{1\,+\,t^2}$
Is it $\frac{d^2x}{dt^2}\,+\,x\,=\,10e^{2t}$ ?

General solution should be:

$x(t)=2e^{2t}+A\sin{t}+B\cos{t}$

 November 21st, 2010, 12:57 PM #12 Senior Member   Joined: Oct 2010 Posts: 126 Thanks: 0 Re: Differential Equations Thanks stainburg and skipjack!

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