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Popular >

y^'+(7y)/(x+3)=(x+3)^3

Solution

y^{^{'}} + \frac{7 y}{x + 3} = (x + 3)^{3}

Solution

y = \frac{x ^{11}}{11 ( x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187 )} + \frac{3 x ^{10}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{45 x ^{9}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{405 x ^{8}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{2430 x ^{7}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{10206 x ^{6}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{30618 x ^{5}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{65610 x ^{4}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{98415 x ^{3}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{98415 x ^{2}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{59049 x}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{c _{1}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187}

Solution steps

y^{'} (x) + \frac{7 y}{x + 3} = (x + 3)^{3}

Solve linear ODE:

y = \frac{x ^{11}}{11 ( x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187 )} + \frac{3 x ^{10}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{45 x ^{9}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{405 x ^{8}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{2430 x ^{7}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{10206 x ^{6}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{30618 x ^{5}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{65610 x ^{4}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{98415 x ^{3}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{98415 x ^{2}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{59049 x}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{c _{1}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187}

y = \frac{x ^{11}}{11 ( x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187 )} + \frac{3 x ^{10}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{45 x ^{9}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{405 x ^{8}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{2430 x ^{7}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{10206 x ^{6}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{30618 x ^{5}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{65610 x ^{4}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{98415 x ^{3}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{98415 x ^{2}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{59049 x}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187} + \frac{c _{1}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187}

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Frequently Asked Questions (FAQ)

What is the solution for y^'+(7y)/(x+3)=(x+3)^3 ?
The solution for y^'+(7y)/(x+3)=(x+3)^3 is