What is the solution for (dy)/(dx)+(3/x)y=-2x+7 ?

The solution for (dy)/(dx)+(3/x)y=-2x+7 is y=-(2x^2)/5+(7x)/4+(c_{1})/(x^3)

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(dy)/(dx)+(3/x)y=-2x+7

\frac{d y}{d x} + (\frac{3}{x}) y = - 2 x + 7

y = - \frac{2 x ^{2}}{5} + \frac{7 x}{4} + \frac{c _{1}}{x ^{3}}

Solution steps

\frac{d y}{d x} + (\frac{3}{x}) y = - 2 x + 7

Solve linear ODE:

y = - \frac{2 x ^{2}}{5} + \frac{7 x}{4} + \frac{c _{1}}{x ^{3}}

y = - \frac{2 x ^{2}}{5} + \frac{7 x}{4} + \frac{c _{1}}{x ^{3}}

x \to - 1 lim (1 + 2 x)

100 y^{^{''}} + 60 y^{^{'}} - 27 y = 0

7 x, \frac{7}{4} x, 78 - x^{2}, y = 0

y^{^{''}} + 2 \cdot y^{^{'}} + 26 \cdot y = e^{- x} cos (5 \cdot x)

What is the solution for (dy)/(dx)+(3/x)y=-2x+7 ?
The solution for (dy)/(dx)+(3/x)y=-2x+7 is y=-(2x^2)/5+(7x)/4+(c_{1})/(x^3)