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# MATH HW 1 - Name:lker Kksal ID:20800584 Section:02 MATH 225...

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Name: İlker Köksal ID: 20800584 Section: 02 MATH 225 Spring 2010 – 2011 MATLAB HOMEWORK #1 1-) a-) ans = dsolve('Dy + 2*y/x = sin(x)/x^2','x') ans = -(C2 + cos(x))/x^2 While I am using ‘dsolve’ I found the general solution of the first order differential equation. b-) I draw the solution curves for three initial values that I choose and I used ‘ezplot()’ to solve this.

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*-) ans = dsolve('Dy + 2*y/x = sin(x)/x^2','y(1)= 5','x') ans = (cos(1) - cos(x) + 5)/x^2 >> ezplot(ans)
*-) ans = dsolve('Dy + 2*y/x = sin(x)/x^2','y(5)= 50','x') ans = (cos(5) - cos(x) + 1250)/x^2 >> ezplot(ans)

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>> ans = dsolve('Dy + 2*y/x = sin(x)/x^2','y(50)= 200','x') ans = (cos(50) - cos(x) + 500000)/x^2 >> ezplot(ans)
c-)While I am using “dfield”, I draw the direction field of the equation in (a). d-) In conclusion, in part c, the graph includes all solutions but in part b, the graphs are drawn with three initial values that I chose. 2-) a-) >> ans = dsolve('Dy = 2*x*(1 + y^2)','x') ans = i -i tan(x^2 + C14) While I am using ‘dsolve’ I found the general solution of the first order differential equation.

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MATH HW 1 - Name:lker Kksal ID:20800584 Section:02 MATH 225...

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