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Popular Calculus >

(x+1)(dy)/(dx)-x+4y=0

Solution

(x + 1) \frac{d y}{d x} - x + 4 y = 0

Solution

y = \frac{x ^{5}}{5 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )} + \frac{3 x ^{4}}{4 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )} + \frac{x ^{3}}{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1} + \frac{x ^{2}}{2 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )} + \frac{c _{1}}{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1} - \frac{1}{20 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )}

Solution steps

(x + 1) \frac{d y}{d x} - x + 4 y = 0

Solve linear ODE:

y = \frac{x ^{5}}{5 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )} + \frac{3 x ^{4}}{4 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )} + \frac{x ^{3}}{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1} + \frac{x ^{2}}{2 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )} + \frac{c _{1}}{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1} - \frac{1}{20 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )}

y = \frac{x ^{5}}{5 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )} + \frac{3 x ^{4}}{4 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )} + \frac{x ^{3}}{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1} + \frac{x ^{2}}{2 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )} + \frac{c _{1}}{x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1} - \frac{1}{20 ( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x + 1 )}

Graph

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Frequently Asked Questions (FAQ)

What is the solution for (x+1)(dy)/(dx)-x+4y=0 ?
The solution for (x+1)(dy)/(dx)-x+4y=0 is