What is the solution for (1+y^2)cos(x)dx-1/x dy=0,y(0)= pi/4 ?

The solution for (1+y^2)cos(x)dx-1/x dy=0,y(0)= pi/4 is y=tan(xsin(x)+cos(x)+c_{1})

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(1+y^2)cos(x)dx-1/x dy=0,y(0)= pi/4

(1 + y^{2}) cos (x) d x - \frac{1}{x} d y = 0, y (0) = \frac{π}{4}

y = tan (x sin (x) + cos (x) + c_{1})

Solution steps

(1 + y^{2}) cos (x) d x - \frac{1}{x} d y = 0

Solve separable ODE:

y = tan (x sin (x) + cos (x) + c_{1})

y = tan (x sin (x) + cos (x) + c_{1})

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

\frac{d x}{d t} = a x

d x - (8 x y + 3 y) d y = 0

(y^{2} + 1) sin (x) d x - y cos (x) d y = 0, y (0) = 0

\frac{d y}{d x} = \frac{y}{2 x + 1}

What is the solution for (1+y^2)cos(x)dx-1/x dy=0,y(0)= pi/4 ?
The solution for (1+y^2)cos(x)dx-1/x dy=0,y(0)= pi/4 is y=tan(xsin(x)+cos(x)+c_{1})