Mathematics
IvelisseBilello491
2015-11-03 23:51:54
Solve the given initial-value problem. give the largest interval i over which the solution is defined. x dy dx + y = 6x + 1, y(1) = 8
ANSWERS
zmckeown1199
2015-11-04 00:04:53

[latex]xdfrac{mathrm dy}{mathrm dx}+y=6x+1[/latex] [latex]dfrac{mathrm d}{mathrm dx}(xy)=6x+1[/latex] [latex]xy=displaystyleint(6x+1),mathrm dx[/latex] [latex]xy=3x^2+x+C[/latex] Given that [latex]y(1)=8[/latex], we have [latex]8=3+1+Cimplies C=4[/latex] so that the particular solution is [latex]xy=3x^2+x+4[/latex] [latex]y=3x+1+dfrac4x[/latex] which is valid as long as [latex]x eq0[/latex], which in turn suggests the largest interval over which the solution may be valid is [latex](0,infty)[/latex].

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