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This is kinda a typical question of. But I'm really stuck in this.

Is there any one how to solve thisquestion. Really really appreciate it.

Pe.
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  • Hi @arjafi, I believe the conversation contains lots of meaningful and useful info. Would you mind put some selected comments back so other beginners could benefit? Thanks! – Pe. May 14 '17 at 05:51

1 Answers1

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The optimal $y$ in the functional $$\int_a^b L(y,y',x)\, dx$$ must satisfy the Euler-Lagrange equation: $$\frac{\partial L}{\partial y} - \frac{d}{dx}\frac{\partial L}{\partial y'} = 0$$ Here, we have $L(y,y',x) = (y')^2+12xy$. Plugging this into the ELE gives us $$12x - \frac{d}{dx}(2y') = 12x - 2y'' = 0$$ i.e. $$y'' = 6x$$ and so $$y = x^3+c_1 x+c_2$$ for some constants $c_1, c_2$ which you can solve for using $y(0) = 0, y(1)=1$.

florence
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