Nonlinear method for boundary value problems of a constant function.

**Marcorupert** · October 16th 2012, 09:58 AM

the question Im having a hard time dealing with is this equation
y"(t)=-g where g is the gravity at 9.8m/s^2
and the boundaries are
y(0)=0.9144 and y(3)=0

how to solve this problem? I am having trouble with runge kutta since it is only a constant function? what to do pls?
I need to know how many shots to and the graph. thanks

**Soroban** · October 16th 2012, 11:50 AM

Hello, Marcorupert!

From your title, you're making the problem sound trickier than it is.

$y"(t)\,=\,\text{-}g\;\text{ where }g\text{ is the accel'n due to gravity at }9.8\text{m/s}^2$

$\text{and the initial conditions are: }\,y(0)\,=\,0.9144\,\text{ and }\,y(3)\,=\,0 .$

$\text{Find }y(t).$

We have: . $y''(t) \:=\:\text{-}9.8$

Integrate: . $y'(t) \:=\:\text{-}9.8t + C_1$

Integrate: . $y(t) \:=\:\text{-}4.9t^2 + C_1t + C_2$

We are told that $y(0) = 0.9144\!:$
. . $\text{-}4.9(0^2) + C_1(0) + C_2 \:=\:0.9144 \quad\Rightarrow\quad C_2 \,=\,0.9144$

We are told that $y(3) = 0\!:$
. . $\text{-}4.9(3^2) + C_1(3) + 0.9144 \:=\:0 \quad\Rightarrow\quad C_1 \,=\,14.3952$

Therefore: . $y(t) \;=\;\text{-}4.9t^2 + 14.3952t + 0.9144$

**Marcorupert** · October 16th 2012, 08:30 PM

Thanks But I need to know the first shot of the graph in nonlinear method. :/

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