Consider the first order ODE dy = = f(x, y) = x + y. dx (a)...
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Consider the first order ODE dy = = f(x, y) = x + y. dx (a) Sketch the slope field in the x, y-plane. (b) One of the solution curves is a straight line. Find the equation of this line. [Hint: Suppose that y = mx + b for some constants m and b. Then we have dy m = = x+y=x+mx+b. dx Hence the equation m = x + mx + b holds for any value of x. Use this to solve for m and b.] Consider the first order ODE dy = = f(x, y) = x + y. dx (a) Sketch the slope field in the x, y-plane. (b) One of the solution curves is a straight line. Find the equation of this line. [Hint: Suppose that y = mx + b for some constants m and b. Then we have dy m = = x+y=x+mx+b. dx Hence the equation m = x + mx + b holds for any value of x. Use this to solve for m and b.]
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Related Book For
An Introduction to Geotechnical Engineering
ISBN: 978-0132496346
2nd edition
Authors: Robert D. Holtz, William D. Kovacs, Thomas C. Sheahan
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