What is the solution for sqrt(10-x^2)y^'=e^{6y}sin(x) ?

The solution for sqrt(10-x^2)y^'=e^{6y}sin(x) is y=-(ln(-6*integral of (sin(x))/(sqrt(10-x^2))))/6

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sqrt(10-x^2)y^'=e^{6y}sin(x)

10 - x^{2} y^{^{'}} = e^{6 y} sin (x)

y = - \frac{ln ( - 6 \cdot \int \frac{s i n ( x )}{10 - x ^{2}} d x )}{6}

Solution steps

10 - x^{2} y^{'} (x) = e^{6 y} sin (x)

Solve separable ODE:

y = - \frac{ln ( - 6 \cdot \int \frac{s i n ( x )}{10 - x ^{2}} d x )}{6}

y = - \frac{ln ( - 6 \cdot \int \frac{s i n ( x )}{10 - x ^{2}} d x )}{6}

y^{^{'}} + (x + 4) y = 0

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

x y^{^{'}} - 3 y = k

\frac{d x}{d y} - 2 x = 6

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

What is the solution for sqrt(10-x^2)y^'=e^{6y}sin(x) ?
The solution for sqrt(10-x^2)y^'=e^{6y}sin(x) is y=-(ln(-6*integral of (sin(x))/(sqrt(10-x^2))))/6