Please solve the following, provide well explained and readable solution. x" +5 t (x')2 +3x = t? + 1, x(0) = 1, x'(0) = 2%3DUsing the Euler method with a time step of At = 0.3approximate x(0.6). Do your calculations to at least 4 decimal places of accuracy.

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Description: Please solve the following, provide well explained and readable solution. x" +5 t (x')2 +3x = t? + 1, x(0) = 1, x'(0) = 2%3DUsing the Euler method with a time step of At = 0.3approximate x(0.6). Do your calculations to at least 4 decimal places of ac

x"+5tx'2+3x=t2+1..............1x0=1 , x'0=2Let dxdt=yd2xd2t=dydtNow equation 1 can be written as…

Answered: x" +5 t (x')² + 3x =t2 + 1, x(0) = 1,…

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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Please solve the following, provide well explained and readable solution.

x" +5 t (x')2 +3x = t? + 1, x(0) = 1, x'(0) = 2
%3D
Using the Euler method with a time step of At = 0.3
approximate x(0.6). Do your calculations to at least 4 decimal places of accuracy.

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Step 1

$x^{"} + 5 t {(x^{'})}^{2} + 3 x = t^{2} + 1 . . . . . . . . . . . . . . (1) x (0) = 1, x^{'} (0) = 2 L e t \frac{d x}{d t} = y \frac{d^{2} x}{d^{2} t} = \frac{d y}{d t} N o w e q u a t i o n (1) c a n b e w r i t t e n a s \frac{d y}{d t} = t^{2} + 1 - 3 x - 5 t y^{2} A l s o y (0) = x^{'} (0) = 2 N o w, w e h a v e c o u p l e d e q u a t i o n g i v e n a s \frac{d x}{d t} = y = f_{1} (t, x, y), x (0) = 1 \frac{d y}{d t} = t^{2} + 1 - 3 x - 5 t y^{2} = f_{2} (t, x, y), y (0) = 2$

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