u-R-R-v-R-R-u-dv-dx-v-du-dx-

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Question Number 297 by 123456 last updated on 25/Jan/15

$$u:\mathbb{R}\to \mathbb{R}$$$$v:\mathbb{R}\to \mathbb{R}$$$$\{\begin{array}{l}u=\frac{dv}{dx}\\ v=\frac{du}{dx}\end{array}$$

Answered by prakash jain last updated on 19/Dec/14

$$u=\frac{dv}{dx}=\frac{d^{2}u}{{dx}^2}$$$$u^{″}-u=0$$$${\lambda }^2-1=0$$$$\lambda =\pm 1$$$$u=c_1{e}^x+c_2{e}^{-x}$$$$\frac{du}{dx}=c_1{e}^x-c_2{e}^{-x}=v$$$$\frac{dv}{dx}=c_1{e}^x+c_2{e}^x=u$$$$\mathrm{Solution}$$$$u=c_1{e}^x+c_2{e}^{-x},v=c_1{e}^x-c_2{e}^{-x}$$$$$$

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