##### Question

# y(t–(y(t))2 + 10000-10000e-5t computed with ode45. Prove that the method is unconditionally stable or derive the condition for conditional stability (as a condition for for the ODE for λ <…

y(t–(y(t))2 + 10000-10000e-5t

computed with ode45. Prove that the method is unconditionally stable or derive the condition for conditional stability (as a condition for for the ODE for λ < 0. (b)

y(t–(y(t))2 + 10000-10000e-5t

computed with ode45. Prove that the method is unconditionally stable or derive the condition for conditional stability (as a condition for for the ODE for λ

## Solutions

##### Expert Solution

-5t- dy dt dt st

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n own deep Sope field:

Slope field 1.0 0.5 0.0 -0.5 1.0 1.0-0.5 0.0 0.5 1.0

Plots of sample individual solution: y(0) 1 Sample solution family: 800 600 400 200 (sampling yo) 0.0020.0040.0060.0080.0100.0120.014

Y'(t) DtbevenHal eauaton sol-tion! dx(t) Let Caush on ぴ1tererkad euaH-מ çola.ha.

Slope field: 6 I- 6-42 024 6 Plots of sample individual solution: Sample solution family 12 10 sampling yO 0.5 1.0 1,5 2.0 2.5

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