btcq.net
当前位置:首页 >> yDx x 2 4x Dy 0 >>

yDx x 2 4x Dy 0

求微分方程 ydx+(x²-4x)dy=0的通解 解:ydx=(4x-x²)dy 分离变量得dy/y=dx/(4x-x²) 取积分得lny=∫dx/[x(4-x)]=(1/4)∫[(1/x)+1/(4-x)]dx=(1/4)(lnx-ln(4-x)+lnc lny=(1/4)ln[x/(4-x)]+lnc=lnc[x/(4-x)]^(1/4) 故得通解:y=c[x/(4-x...

dy/y = dx/(4x-x^2) =dx/(1/4(1/x+1/(4-x))) 两边同时积分得 lny=1/4(lnx+ln(4-x))+lnc y=c(x(4-x))^1/4

ydx=(4x-x^2)dy dy/y=dx/(4x-x^2) 两边积分,得ln|y|=∫dx/(4x-x^2) ln|y|=-∫1/[x(x-4)]dx ln|y|=-1/4∫[1/x-1/(x-4)]dx ln|y|=-1/4[lnx-ln(x-4)]+C y=[x/(x-4)]^(1/4)*e^C

4ydx+(4x+1)dy=(4ydx+4xdy)+1dy=4d(xy)+1dy 积分以后就是4xy+y。 注意d(xy)=ydx+xdy

解:∵(y+x)dy-ydx=0 ==>ydy+xdy-ydx=0 ==>dy/y-(ydx-xdy)/y^2=0 (等式两端同除y^2) ==>dy/y-d(x/y)=0 ==>∫dy/y-∫d(x/y)=0 ==>ln│y│-x/y=ln│C│ (C是积分常数) ==>ye^(-x/y)=C ==>y=Ce^(x/y) ∴原方程的通解是y=Ce^(x/y)。

解:∵(2x-y^2)dy-ydx=0 ==>ydx-2xdy+y^2dy=0 ==>(ydx-2xdy)/y^3+dy/y=0 (等式两端同除y^3) ==>∫(ydx-2xdy)/y^3+∫dy/y=0 ==>x/y^2+ln│y│=C (C是积分常数) ==>x=(C-ln│y│)y^2 ∴此方程的通解是x=(C-ln│y│)y^2。

解:∵(x+y)dy–ydx=0 ==>ydy-(ydx-xdy)=0 ==>dy/y-(ydx-xdy)/y^2=0 (等式两端同除y^2) ==>dy/y-d(x/y)=0 ==>ln│y│-x/y=ln│C│ (C是常数) ==>ye^(-x/y)=C ==>y=Ce^(x/y) ∴原方程的通解是y=Ce^(x/y)。

解: (1)点A在抛物线上,于是 m^2=8p, 抛物线的准线方程为:y=-p/2, 点A到其焦点的距离与到准线的距离相等,故 4+p/2=17/4, 由上面两个式子可得:p=1/2,m=2。 (2)抛物线方程为y=x^2。P点坐标为P(t, t^2),设Q(x1, x1^2)、M(m, 0)、N(x2, x2^2)...

用格林公式:奇点(0,0)不在积分域内. I = ∮L (ydx - xdy)/(x^2 + y^2) = ∫∫D [(x^2 - y^2)/(x^2 + y^2)^2 - (x^2 - y^2)/(x^2 + y^2)^2] dxdy = 0 用参数方程. { x = 1 + cost、dx = - sint dt { y = 1 + sint、dy = cost dt 0 ≤ t ≤ 2π ∮L (ydx...

网站首页 | 网站地图
All rights reserved Powered by www.btcq.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com