What is the solution for (1+cos^2(x))y^'+2ycos(x)sin(x)=0 ?

The solution for (1+cos^2(x))y^'+2ycos(x)sin(x)=0 is y=e^{c_{1}}+e^{c_{1}}cos^2(x)

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(1+cos^2(x))y^'+2ycos(x)sin(x)=0

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

y = e^{c_{1}} + e^{c_{1}} cos^{2} (x)

Solution steps

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

Solve separable ODE:

y = e^{c_{1}} + e^{c_{1}} cos^{2} (x)

y = e^{c_{1}} + e^{c_{1}} cos^{2} (x)

What is the solution for (1+cos^2(x))y^'+2ycos(x)sin(x)=0 ?
The solution for (1+cos^2(x))y^'+2ycos(x)sin(x)=0 is y=e^{c_{1}}+e^{c_{1}}cos^2(x)