Question (1 point) Consider the differential equation dy = 6x, dx with initial condition y(0) = 2. A. Use Euler's method with two steps to estimate y when x = 1: y(1) (Be sure not to round your calculations at each step!) Now use four steps: y(1) (Be sure not to round your calculations at each step!) B. What is the solution to this differential equation (with the given initial condition)? y = C. What is the actual value of y(1) for this IVP? Use the solution you found in B. y =
MCZSMI The Asker · Advanced Mathematics
Transcribed Image Text: (1 point) Consider the differential equation dy = 6x, dx with initial condition y(0) = 2. A. Use Euler's method with two steps to estimate y when x = 1: y(1) (Be sure not to round your calculations at each step!) Now use four steps: y(1) (Be sure not to round your calculations at each step!) B. What is the solution to this differential equation (with the given initial condition)? y = C. What is the actual value of y(1) for this IVP? Use the solution you found in B. y =
More Transcribed Image Text: (1 point) Consider the differential equation dy = 6x, dx with initial condition y(0) = 2. A. Use Euler's method with two steps to estimate y when x = 1: y(1) (Be sure not to round your calculations at each step!) Now use four steps: y(1) (Be sure not to round your calculations at each step!) B. What is the solution to this differential equation (with the given initial condition)? y = C. What is the actual value of y(1) for this IVP? Use the solution you found in B. y =
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( ) given ODsqrtzquad(dy)/(dx)=6x,y(0)=2(A) two steps n=2,y(1)= ?h=(1-0)/(2)=(1)/(2)y_(n+1)=y_(n)+hf(x,y_(n)) step-1- h=(1)/(2),x_(0)=0,y_(0)=2,f(x,y)=6xEuler Method states that{:[(" step-1- ")/(x)x_(1)=x_(0)+h=0+(1)/(2)=(1)/(2)],[y((1)/(2))=y0+hf(x0,y_(0))],[=2+(1)/(2)xx6xx0=2],[x_(2)=x+h=(1)/(2)+(1)/(2)=1],[y(x_(2))=y(1)=y_(1)+hf(x_(1),y_(1))","x_(1)=(1)/(2)],[y(1)=2+(1)/(2)xx6xx(1)/(2)=2+(3)/(2)],[y(1)=3.5]:}(1) Now using four step quad h=(1-0)/(4)=(1)/(4)step-1- quad x0=0,y_(0)=2. quad xy=x0+h=(1)/(4) Scanned y(x)=y((1)/(4))=2+(1)/(4)xx f(0,2)=2 CamScannerstef x_(2)=x_(1)+h=(1)/(4)+(1)/( ... See the full answer