Consider the IVP: x" + (x')? + 6tx = 0, x(0) = 3, x'(0) = 4 Using the Euler method with a time step of At = 0.4 approximate x(0.8) to the nearest thousandth (3 decimal places). In the answer box just put the approximation, nothing else.
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a) Please provide a correct and well explained solution for the following;
![**Problem Statement:**
Consider the Initial Value Problem (IVP):
\[ x'' + (x')^2 + 6tx = 0, \quad x(0) = 3, \quad x'(0) = 4 \]
Using the Euler method with a time step of:
\[ \Delta t = 0.4 \]
Approximate \( x(0.8) \) to the nearest thousandth (3 decimal places). In the answer box just put the approximation, nothing else.
**Notation:**
- \( x = x(t) \)
- \( x' = \frac{dx}{dt} \)
- \( x'' = \frac{d^2x}{dt^2} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d945e56-c5e1-480a-9c03-390d785d9d79%2F4623fe66-2393-4ee8-8778-948cc1f3bd16%2Fqv01i5u_processed.jpeg&w=3840&q=75)
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