What is the solution for (1+x^2)y+xy^'+ax=0 ?

The solution for (1+x^2)y+xy^'+ax=0 is y=-a/x+(c_{1}}{e^{\frac{x^2)/2}x}

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(1+x^2)y+xy^'+ax=0

(1 + x^{2}) y + x y^{^{'}} + a x = 0

y = - \frac{a}{x} + \frac{c _{1}}{e ^{\frac{x ^{2}}{2}} x}

Solution steps

(1 + x^{2}) y + x y^{'} (x) + a x = 0

Solve linear ODE:

y = - \frac{a}{x} + \frac{c _{1}}{e ^{\frac{x ^{2}}{2}} x}

y = - \frac{a}{x} + \frac{c _{1}}{e ^{\frac{x ^{2}}{2}} x}

k \to 0 lim (\frac{x ^{2} k + 3 x k ^{2} + k ^{3}}{2 x k + 5 k ^{2}})

\frac{d}{d x} (\frac{1 + x}{1 + e ^{x}})

x^{2} y^{^{''}} + 9 x y^{^{'}} + 16 y = 0

f (x) = sin (5 x)

x \to - 3 lim (- x^{2} + 6 x - 2)

What is the solution for (1+x^2)y+xy^'+ax=0 ?
The solution for (1+x^2)y+xy^'+ax=0 is y=-a/x+(c_{1}}{e^{\frac{x^2)/2}x}