Question

dy/dx=(y+5)(x+2) y(0)=1 求

Answer 1

dy/dx=(y+5)(x+2)

dy/(y+5)=(x+2)dx

两边同时积分

ln(y+5)=x^2/2+2x+C

又如：y(0)=1

即：x=0,y=1

带入ln(y+5)=x^2/2+2x+C

解得：C=ln6

ln(y+5)=x^2/2+2x+ln6

y+5=e^(x^2/2+2x+ln6)

y=6e^(x^2/2+2x)-5