求微分方程dx/y+dy/x=0满足条件y(3)=4的特解?求过程!

Question

求微分方程 dx/y+dy/x=0 满足条件y(3)=4的特解? 求过程!

Answer 1

dx/y+dy/x=0 化为：x dx + y dy = 0
积分：x²/2 + y²/2 = C1
即 x² + y² = C
y(3)=4,带入上式,得：C = 25
特解为：x² + y² = 25