What is the solution for (x^2+36)y^'+xy=x ?

The solution for (x^2+36)y^'+xy=x is y=(c_{1})/(sqrt(x^2+36))+1

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(x^2+36)y^'+xy=x

(x^{2} + 36) y^{^{'}} + x y = x

y = \frac{c _{1}}{x ^{2} + 36} + 1

Solution steps

(x^{2} + 36) y^{'} (x) + x y = x

Solve separable ODE:

y = \frac{c _{1}}{x ^{2} + 36} + 1

y = \frac{c _{1}}{x ^{2} + 36} + 1

\frac{d y}{d x} = - \frac{( x - 8 )}{64 y - 320}

csc (y) + sec^{2} (x) \frac{d y}{d x} = 0

(y + 5) d x + (x - 7) d y = 0

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

\frac{d y}{d x} = - y (x^{2} + 4)

What is the solution for (x^2+36)y^'+xy=x ?
The solution for (x^2+36)y^'+xy=x is y=(c_{1})/(sqrt(x^2+36))+1