Need to solve this the correct way for test prep please **Runge-Kutta 2nd Order Method Application**Apply the Runge-Kutta 2nd order method (by hand) to the following equation with a step size of $ h = 0.15 \, \text{s} $. Find values for $ y(t) $ and $ \dot{y}(t) $ at $ t = 0.15 \, \text{s} $ and $ t = 0.3 \, \text{s} $. Be sure to show your calculations in detail.\[ 100y'' + 700 - 1200y = 250t \]with $ y(0) = 0.5 $ and $ y'(0) = 2 $.**Table: Runge-Kutta Calculations**| $ t $ | $ k_{1,z_1} $ | $ k_{1,z_2} $ | $ k_{2,z_1} $ | $ k_{2,z_2} $ | $ z_1 $ | $ z_2 $ ||---------|---------------|---------------|---------------|---------------|----------|----------|| 0 | - | - | - | - | 0.5 | 2 || 0.1 | | | | | | || 0.2 | | | | | | |Ensure that you perform and document each step of the calculation. Use this structured table to fill in each necessary value derived from the equations.

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Description: Need to solve this the correct way for test prep please **Runge-Kutta 2nd Order Method Application**Apply the Runge-Kutta 2nd order method (by hand) to the following equation with a step size of $ h = 0.15 \, \text{s} $. Find values for $ y(t) $

Given the expression is , 100y-700-1200y=250t , y(0)=0.5 , h=0.15 find out the value of y(0.15).

Math

Advanced Math

Apply the Runge-Kutta 2nd order method (by hand) to the following equation with a step size of h = 0.15 s. Find values for y(t) and y (t) at t = 0.15 s and t = 0.3 s. Be sure to show your calculations in detail. %3D %3D 100y" + 700 – 1200y = 250t with y(0) = 0.5 and y'(0) = 2 %3D k2,71 k2,z2 Z2 k1,1 k122 Z1 0.5 0.1 2.

Apply the Runge-Kutta 2nd order method (by hand) to the following equation with a step size of h = 0.15 s. Find values for y(t) and y (t) at t = 0.15 s and t = 0.3 s. Be sure to show your calculations in detail. %3D %3D 100y" + 700 – 1200y = 250t with y(0) = 0.5 and y'(0) = 2 %3D k2,71 k2,z2 Z2 k1,1 k122 Z1 0.5 0.1 2.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Need to solve this the correct way for test prep please

**Runge-Kutta 2nd Order Method Application**

Apply the Runge-Kutta 2nd order method (by hand) to the following equation with a step size of $ h = 0.15 \, \text{s} $. Find values for $ y(t) $ and $ \dot{y}(t) $ at $ t = 0.15 \, \text{s} $ and $ t = 0.3 \, \text{s} $. Be sure to show your calculations in detail.

\[ 100y'' + 700 - 1200y = 250t \]

with $ y(0) = 0.5 $ and $ y'(0) = 2 $.

**Table: Runge-Kutta Calculations**

| $ t $ | $ k_{1,z_1} $ | $ k_{1,z_2} $ | $ k_{2,z_1} $ | $ k_{2,z_2} $ | $ z_1 $ | $ z_2 $ |
|---------|---------------|---------------|---------------|---------------|----------|----------|
| 0 | - | - | - | - | 0.5 | 2 |
| 0.1 | | | | | | |
| 0.2 | | | | | | |

Ensure that you perform and document each step of the calculation. Use this structured table to fill in each necessary value derived from the equations.

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