Question

Решить задачу Коши: yy'=1+x^2 , y(1)=1

Answer 1

yy'=1+x² , y(1)=1

ydy = (1 + x²)dx

∫ydy = ∫(1 + x²)dx

0,5y² = x + x³/3 + C

0,5 = 1 + 1/3 + C

C = -5/6

0,5y² = x + x³/3 - 5/6

y² = 2x + 2x³/3 - 5/3

y = √(2x + 2x³/3 - 5/3)