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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Solve separable ODE:

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

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

Graph

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y^'+sqrt(x-x^2)*y=sqrt(x-x^2)

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Frequently Asked Questions (FAQ)

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