Answer
f(x)=e^{(x^2)/2}+1
Work Step by Step
f(x)=y
f'(x)=dy/dx
dy/dx=xy-x <=> dy/dx=x(y-1) <=> \int1/(y-1)dy=\intxdx <=>ln(y-1)=(x^2)/2+C <=>y=e^((x^2)/2+C)+1
y(0)=2
2-1=e^(0+C) <=> 1=e^C <=>C=0
y=e^((x^2)/2)+1
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 9 - Section 9.3 - Separable Equations - 9.3 Exercises - Page 605: 20
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