∵(y²-3x²)dy+2xydx=0
∴((y/x)²-3)dy+2(y/x)dx=0.(1)
设t=y/x,则dy=xdt+tdx
代入(1)得(t²-3)(xdt+tdx)+2tdx=0
==>x(t²-3)dt+(t³-t)dx=0
==>(t²-3)dt/(t-t³)=dx/x
==>[1/(1+t)-1/(1-t)-3/t]dt=dx/x
==>ln│1+t│+ln│1-t│-3ln│t│=ln│x│+ln│C│ (C是积分常数)
==>(1-t²)/t³=Cx
==>(1-(y/x)²)/(y/x)³=Cx
==>(x²-y²)/y³=C
==>x²-y²=Cy³
∵当x=0时,y=1
∴0²-1²=C*1³ ==>C=-1
故原微分方程满足x=0,y=1时的特解是x²-y²=-y³,即x²-y²+y³=0.
求微分方程(y^2-3x^2)dy+2xydx=0 x=0,y=1时的特解
求微分方程(y^2-3x^2)dy+2xydx=0 x=0,y=1时的特解
数学人气:194 ℃时间:2019-08-26 06:57:16
优质解答
我来回答
类似推荐
猜你喜欢
- 121.Not until I began to work __________how much time I had wasted.A.didn
- 2thank you very much 和 thank your very much
- 31——3000这3000个连续自然数的所有数字之和.
- 4蒸发结晶和冷却结晶有什么不同?
- 5一辆汽车从甲地开往乙地,第一小时行了全程的七分之一,第二小时比第一小时多行了16千米,这时距乙地还
- 6Rose __to school very early every day. A.arrives B.gets C. reaches
- 7分数单位是八分之一的所有最简真分数的和是多少
- 8苯乙烯与氢气的反应
- 9点P是正方形ABCD内的一点,连结PA、PB、PC,将△PAB绕点B顺时针旋转90°到△ECB的位置.
- 10Would you like _____,please?A.two glass of water B.two glasses of water C.two glass of waters