Plotting families of solutions:
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print(); # input placeholder
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print(); # input placeholder
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%;
JSFH
Automated Variation of Parameters:
Consider the differential equation y'' + y = tan(x). The indepenent complementary
solutions to this equation are y1=cos(x) and y2=sin(x).
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print(); # input placeholder
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
print(); # input placeholder
Use the variation of parameters formula to compute the particular solution yp in Maple:
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
print(); # input placeholder
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print(); # input placeholder
Solving differential equations in Maple:
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
print(); # input placeholder
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
print(); # input placeholder
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
print(); # input placeholder
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
%;
JSFH
Laplace Transforms in Maple:
QyQtSSV3aXRoRzYiNiNJKWludHRyYW5zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlISIi
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
print(); # input placeholder
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print(); # input placeholder
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print(); # input placeholder
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print(); # input placeholder
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print(); # input placeholder
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print(); # input placeholder
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print(); # input placeholder
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print(); # input placeholder
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print(); # input placeholder
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print(); # input placeholder
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