![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step1.JPG\")
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(a).
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The graph a slope field for the differential equation ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=81277ea5850e3ec69ae49b0aafb67ef5.png\")
is shown in below figure.
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![\"graph](\"http://www.mathskey.com/userfiles/image/Library/calculus/graph_the_differential_equation_dy_by_dx=2x.gif\")
![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step2.JPG\")
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(b).
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The differential equation is and the point is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=006a9ab1fe1d5f988142e8ea2a12d796.png\")
.
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Multiply each side by ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=81ef740b7ec7a4285fb71244ec402f5d.png\")
.
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![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=852a4fbab9d0c5dc77ed6d59ba51aff7.png\")
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Apply integration on both sides.
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![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=c11de38163cc349dd4852f9b5959df8a.png\")
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![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=1439763bd012f35e59f5a8a859f60038.png\")
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![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=d06423ebd8a1d636f29df20676803647.png\")
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![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a6f7c575c219b187e555ad9a1c701647.png\")
.
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The general solution is .
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To find the value of C, substitute ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=a5eb59396642ef356ba46c747fa1031c.png\")
in the equation .
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![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=efa968c6ede26248a46d96ad08de0ac3.png\")
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![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=e4affbf66048f8f6d39fcb8fa9343fee.png\")
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Subtract 4 from each side
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![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=4244370618c558fd857b174d2874c505.png\")
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The particular solution is ![\"\"](\"http://www.mathskey.com/test/fckeditor/editor/plugins/fckeditor_wiris/integration/showimage.php?formula=d1b918e529cfe2c443c06a727f649b7f.png\")
.
![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/step3.JPG\")
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(c).
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The graph of particular solution and slope field are shown in below figure.
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![\"graph](\"http://www.mathskey.com/userfiles/image/Library/calculus/graph_the_equation_y=x%5E2-6.gif\")
![\"\"](\"http://www.mathskey.com/userfiles/image/steps_images/solution.JPG\")
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(a).
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The graph a slope field for the differential equation is shown in below figure.
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(b).
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The particular solution is .
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(c).
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The graph of particular solution and slope field are shown in below figure.
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