Question

Use Euler's method with step size 0.1 to estimate y(0.2), where y(x) is the solution of the initial-value problem
y'=−5x+y^2,   y(0)=0

y(0.2)=

Answer 1

Euler Method 1) y = F(Xnry, In-1) 2) Y(X) =) 3) Xn = knyth In-It h. F (An-1, In-I) 5) n = 1, 2, 3 4) Yn Geiven :- y = -5x + y2 ,ylo)=0 h = o. 1 (step size] y (0.2) = 2 26=0 Now, y = Noth y = 0 + 0.1 [ X 1 = 0.1 Yn = In-gth. Flans, Inos) Y = 9 (0.1) - Yot 0.1 [~ 5 Xot 4 ] = 0 + 0.1 [-5x0 + 0²] Y(0.1) = 0 + 0x0 Is = 9(0.1)=0 yout=0

Y = Yo.2) = Yy+ 0.4 :1 (-5 Hy + y Ye = Y(0-2) = 0 + 0-4 (-5X0.4+10)2] Ya = Y(0:2) = 0.1[-0.5] 92 = 9 (0.2) = -0.05 an Yn Yo = 9(0)=0 step size h= 0.1 No=0 toil Y = y Co.f)=0 11=0.1 ) tooL Y2=9(0.2) = -0.05 12=0:24

Conclusion :- The value of y(0.2) is -0.05.

I hope it will help you .

Thanks!