Initial Value Problem LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Solve the initial value problem 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 On the same set of axes, obtain a graph of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tRiw2I1EhRidGPQ== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ0RidGL0YyRjlGOUY5. Obtain a graph of the orbit this solution makes in the phase plane. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Control-drag the ODE. Context Menu: Solve DE Interactively Enter the inital data Solve Symbolically Solve Plot Plot Options to obtain desired graphs. JSFH dsolve[':-interactive']( ); LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Expeditious Maple Solution JSFHrestart; interface(typesetting = extended); Typesetting[Settings](useprime, prime = t); with(DEtools,particularsol); Enter the DE 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 Enter the initial conditions 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 Solve the IVP 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 Plot the solution 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 Begin a stepwise solution - Solve the homogeneous ODE Obtain a fundamental set 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 Make the exponential guess LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjeXBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSkmQXNzaWduO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUklbXN1cEdGJDYlLUY2Ni1RLyZFeHBvbmVudGlhbEU7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjExMTExMTFlbUYnLUYjNiUtRiw2JVEpJmxhbWJkYTtGJy9GMEY9RjktRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSEZVL0ZORlYtRiw2JVEidEYnRi9GMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRic= Obtain the characteristic equation 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 Obtain the characteristic roots 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 Fundamental set generated by complex characteristic roots 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 Linear combinations \342\207\222 real fundamental set 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 Obtain a particular solution Obtain a particular solution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmZXZhbGNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUS5wYXJ0aWN1bGFyc29sRidGL0YyLUY2NiQtRiM2JS1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JUZBLyUrYWN0aW9udHlwZUdRO21hcGxlc29mdC5jb206bGFiZWwoTDUyMzcpRicvJSV2aWV3R1EmbGFiZWxGJ0ZBL0YzUSdub3JtYWxGJ0ZN Particular Solution from first principles - the method of Undetermined Coefficients Formal particular solution for method of undetermined coefficients 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 Substitution of particular solution into DE 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 Determine coefficients 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 Alternatively, write equations arising from a match of coefficients of like terms 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 Solve equations for coefficients 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 Write the particular solution 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 Obtain the general solution and apply the initial data Write general solution 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 Apply initial conditions 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 Solve for coefficients in general solution 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 Write specific solution of given IVP 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 Compare to Maple's dsolve solution: 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