What is the solution for y^'+((7x)/(x^2+1))y=(7x)/(x^2+1) ?

The solution for y^'+((7x)/(x^2+1))y=(7x)/(x^2+1) is y=-(c_{1})/((x^2+1)^{7/2)}+1

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y^'+((7x)/(x^2+1))y=(7x)/(x^2+1)

y^{^{'}} + (\frac{7 x}{x ^{2} + 1}) y = \frac{7 x}{x ^{2} + 1}

y = - \frac{c _{1}}{( x ^{2} + 1 ) ^{\frac{7}{2}}} + 1

Solution steps

y^{'} (x) + (\frac{7 x}{x ^{2} + 1}) y = \frac{7 x}{x ^{2} + 1}

Solve separable ODE:

y = - \frac{c _{1}}{( x ^{2} + 1 ) ^{\frac{7}{2}}} + 1

y = - \frac{c _{1}}{( x ^{2} + 1 ) ^{\frac{7}{2}}} + 1

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x \to 0 + lim (\frac{1}{ln ( x )})

What is the solution for y^'+((7x)/(x^2+1))y=(7x)/(x^2+1) ?
The solution for y^'+((7x)/(x^2+1))y=(7x)/(x^2+1) is y=-(c_{1})/((x^2+1)^{7/2)}+1