If the solution y=y(x) of the differential equation (x^4+2 x^3+3 x^2+2 x+2 ) d y- (2 x^2+2 x+3 ) d x=0 satisfies y(-1)=- 4 , then y(0) is equal to :

Step-by-step solution

aligned & d y= (2 x^2+2 x+3 ) x^4+2 x^3+3 x^2+2 x+2 d x & y= (2 x^2+2 x+3 ) (x^2+1 ) (x^2+2 x+2 ) d x & y= d x x^2+2 x+2 + d x x^2+1 & y= ⁻¹(x+1)+ ⁻¹ x+C & y(-1)= - 4 & - 4 =0- 4 +C C=0 & y= ⁻¹(x+1)+ ⁻¹ x & y(0)= ⁻¹ 1= 4 aligned