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Q6) Solve the following differential equation: dy =y-4y2, - by Euler's method (4 steps, h-0.1). y (0) = 0.2

Q6) Solve the following differential equation: dy =y-4y2, - by Euler's method (4 steps, h-0.1). y (0) = 0.2

Advanced Engineering Mathematics
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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Q6) Solve the following differential equation: dy dx by Euler's method (4 steps, h-0.1). = y - 4y², y (0) = 0.2
Transcribed Image Text:Q6) Solve the following differential equation: dy dx by Euler's method (4 steps, h-0.1). = y - 4y², y (0) = 0.2
Expert Solution
Step 1

Sol:-

The step size is h=25-04=110hThe Euler's method states that yn+1=yn+h·ftn,ynyn+1​=yn​+h⋅f(tn​,yn​),where tn+1=tn+htn+1​=tn​+h.We have that h=110h=101​,t0=0 t0​=0,y0=15y0​=51​,and ft,y=-4y2+yf(t,y)=−4y2+y.

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