What is the solution for y-x(dy)/(dx)=a(1+x^2(dy)/(dx)) ?

The solution for y-x(dy)/(dx)=a(1+x^2(dy)/(dx)) is y=-(ac_{1}x)/(1+ax)+a

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y-x(dy)/(dx)=a(1+x^2(dy)/(dx))

y - x \frac{d y}{d x} = a (1 + x^{2} \frac{d y}{d x})

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

Solution steps

y - x \frac{d y}{d x} = a (1 + x^{2} \frac{d y}{d x})

Solve separable ODE:

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

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

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x^{^{''}} + 10 x^{^{'}} + 21 x = 0

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\frac{\partial}{\partial x} (7 y^{6} x^{6} - 6 y^{5} x^{5})

What is the solution for y-x(dy)/(dx)=a(1+x^2(dy)/(dx)) ?
The solution for y-x(dy)/(dx)=a(1+x^2(dy)/(dx)) is y=-(ac_{1}x)/(1+ax)+a