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

The solution for (dy)/(dx)=(y+1)(x+1)cos(x^2+2x),y(0)=4 is y=5e^{1/2 sin(x^2+2x)}-1

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

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

y = 5 e^{\frac{1}{2} s i n (x^{2} + 2 x)} - 1

Solution steps

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

Solve separable ODE:

y = 5 e^{\frac{1}{2} s i n (x^{2} + 2 x)} - 1

y = 5 e^{\frac{1}{2} s i n (x^{2} + 2 x)} - 1

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

\frac{d y}{d x} - \frac{y}{x + 1} = 0

a y^{^{'}} + y = c

(2 y + 2) d y - (4 x^{3} + 6 x) d x = 0

\frac{d x}{d y} = sin (x) (cos (2 y) - cos^{2} (y))

What is the solution for (dy)/(dx)=(y+1)(x+1)cos(x^2+2x),y(0)=4 ?
The solution for (dy)/(dx)=(y+1)(x+1)cos(x^2+2x),y(0)=4 is y=5e^{1/2 sin(x^2+2x)}-1