What is the solution for x/(a^2)+(ydy)/(b^2dx)=0 ?

The solution for x/(a^2)+(ydy)/(b^2dx)=0 is y=(bsqrt(c_{1)-x^2})/a ,y=-(bsqrt(c_{1)-x^2})/a

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x/(a^2)+(ydy)/(b^2dx)=0

\frac{x}{a ^{2}} + \frac{y d y}{b ^{2} d x} = 0

y = \frac{b c _{1} - x ^{2}}{a}, y = - \frac{b c _{1} - x ^{2}}{a}

Solution steps

\frac{x}{a ^{2}} + \frac{y d y}{b ^{2} d x} = 0

Solve separable ODE:

y = \frac{b c _{1} - x ^{2}}{a}, y = - \frac{b c _{1} - x ^{2}}{a}

y = \frac{b c _{1} - x ^{2}}{a}, y = - \frac{b c _{1} - x ^{2}}{a}

cos (y) y^{^{'}} + 2 x sin (y) = - 2 x

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

y^{^{'}} = x y - 4 x, y (0) = 5

y^{^{'}} = y^{3} sin (x)

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

What is the solution for x/(a^2)+(ydy)/(b^2dx)=0 ?
The solution for x/(a^2)+(ydy)/(b^2dx)=0 is y=(bsqrt(c_{1)-x^2})/a ,y=-(bsqrt(c_{1)-x^2})/a