Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 10 - Introduction to Differential Equations - 10.1 Solving Differential Equations - Exercises - Page 505: 35


$$y= 2(1+e^{\frac{1}{2}x^{2}-x}).$$

Work Step by Step

By separation of variables, we have $$\frac{dy}{y-2}=(x-1)dx$$ Then by integration, we get $$\ln(y-2)=\frac{1}{2}x^{2}-x+c\Longrightarrow y=Ae^{\frac{1}{2}x^{2}-x}+2.$$ Now, since $y(2)=4$, then $A=2$. So the general solution is given by $$y= 2(1+e^{\frac{1}{2}x^{2}-x}).$$
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