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Popular Calculus >

(2x+5)y^'+10y=10(2x+5)

Solution

(2 x + 5) y^{^{'}} + 10 y = 10 (2 x + 5)

Solution

y = \frac{10 ( 16 x ^{6} + 240 x ^{5} + 1500 x ^{4} + 5000 x ^{3} + 9375 x ^{2} + 9375 x )}{3 ( 32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125 )} + \frac{c _{1}}{32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125}

Solution steps

(2 x + 5) y^{'} (x) + 10 y = 10 (2 x + 5)

Solve linear ODE:

y = \frac{10 ( 16 x ^{6} + 240 x ^{5} + 1500 x ^{4} + 5000 x ^{3} + 9375 x ^{2} + 9375 x )}{3 ( 32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125 )} + \frac{c _{1}}{32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125}

y = \frac{10 ( 16 x ^{6} + 240 x ^{5} + 1500 x ^{4} + 5000 x ^{3} + 9375 x ^{2} + 9375 x )}{3 ( 32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125 )} + \frac{c _{1}}{32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125}

Graph

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Frequently Asked Questions (FAQ)

What is the solution for (2x+5)y^'+10y=10(2x+5) ?
The solution for (2x+5)y^'+10y=10(2x+5) is