What is the solution for y^'+1/(sqrt(1-x^2))y= 3/(sqrt(1-x^2)) ?

The solution for y^'+1/(sqrt(1-x^2))y= 3/(sqrt(1-x^2)) is y=-e^{-arcsin(x)-c_{1}}+3

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y^'+1/(sqrt(1-x^2))y= 3/(sqrt(1-x^2))

y^{^{'}} + \frac{1}{1 - x ^{2}} y = \frac{3}{1 - x ^{2}}

y = - e^{- a r c s i n (x) - c_{1}} + 3

Solution steps

y^{'} (x) + \frac{1}{1 - x ^{2}} y = \frac{3}{1 - x ^{2}}

Solve separable ODE:

y = - e^{- a r c s i n (x) - c_{1}} + 3

y = - e^{- a r c s i n (x) - c_{1}} + 3

y^{^{'}} - 3 y = - 4

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

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

(2 t - 1) y^{^{'}} - 4 y = 0

\frac{d p}{d t} + 2 tp = p + 8 t - 4

What is the solution for y^'+1/(sqrt(1-x^2))y= 3/(sqrt(1-x^2)) ?
The solution for y^'+1/(sqrt(1-x^2))y= 3/(sqrt(1-x^2)) is y=-e^{-arcsin(x)-c_{1}}+3