2.判断下列方程是否为全微分方程,试用凑微分法或积分因子求解下列方程:(1) (3x^2+2xy^2)dx+(2x^2y+3y^2)dy=0 ;(2)(x+y)dy-ydx=0; (3)xdx+ydy=ydx -xdy. 相关知识点: 试题来源: 解析 2.(1)全微分方程, x^3+y^3+x^2y^2=C .提示:用凑微分 3x^2dx+3y^2dy+ 2xy^2dx+2x^2ydy=...
由已知得原微分方程对应的特征方程为 (dx)/(2xy^2+xz)=(dy)/(-yz-3x^3y)=(dz)/(3x^3z-2y^2z) dy s, s, 于是 (dz)/(3x^3z-2y^2z)=(ydx+xdy)/(xy(2y^2-3x^3)=(3x^3dx+2ydy-dz)/0 由第一式求得首次积分 -(dz)/z=(ydx+xdy)/(xy)=(dx)/x+(dy)/y … 而由第...
du=2dx+3dy,dy=(xdy+ydx)e^xy偏导数符号打不出来.用p代替吧,dz=(pz/pu)du+(pz/pv)dv=(pz/pu)(2dx+3dy)+(pz/pv)(xdy+ydx)e^xy=[2pz/pu+ye^xy pz/pv]dx + [3pz/pu+xe^xy pz/pv]dy 31035 设函数y=f(x)的图像上点(0,-2)处切线为2x-3y=6则此函数可能为___ 2x-3y=6可化为...
Solve the differential equation: (1+x^2) dy/dx + 2xy -4x^2 =0 Solve the differential equation: \frac{d^2y}{dx^2} + \frac{dy}{dx} + 4y = 0 Solve the differential equation y'' + 6y' + 10 y =0 Solve the differential equation (3xy^2+8y^2+12x+32)dx - (4x^2y+20...
Compute the following integrals: Using greens theorem. (a) integral e^(2x + 3y) dx + e^(xy) dy, where D is described by -2<=x<=2,-1<=y<=1 (b) integral ycos(x)dx+ysin(x)xdy, where D is described by 0<...
(5)(x-y2)dx+2xydy=0;(6)2ydx-3xy2dx-xdy=0. 相关知识点: 试题来源: 解析 解(1) 方程两边同时乘以得 ,即d(x-y)=dln(x+y), 所以为原方程的一个积分因子, 并且原方程的通解为 x-y=ln(x+y)+C. (2) 方程两边同时乘以得 ,即, 所以为原方程的一个积分因子, 并且原方程的...
1+2x)1、z=(1+x)^ylnz = yln(1+x)(1/z)dz = ln(1+x) dy + [y/(1+x)].dydz = { ln(1+x) dy + [y/(1+x)].dy} .(1+x)^y 2、dz=xdx+ydy。z=xy，那么dz自然而然等于dxy；dz=(ðz/ðx)dx+(ðz/ðy)dy；=ydx+xdy。3、...
The solution of e^(2x-3y)dx+e^(2y-3x)dy=0 is अवकल समीकरणों को हल कीजिये e2x−3ydx+e2y−3xdy=0 dydx=2x−3y3x−2y dydx=3x+2y2x−3y dydx=2x+3y3x+2y
解：∵(3xy+x^2)dy+(y^2+xy)dx=0==>2y(3xy+x^2)dy+2y(y^2+xy)dx=0(等式两端同乘2y)==>2(3xy^2dy+y^3dx)+2(x^2ydy+xy^2dx)=0==>2d(xy^3)+d(x^2y^2)=0==>2∫d(xy^3)+∫d(x^2y^2)=0==>2xy^3+x^2y^2=C(C是常数)∴此方程的通解是2xy^3+x^2y^2...
dz=f(xy,x+3)dy+y[f1''(ydx+xdy)+f2''(dx+3dy)] =f(xy,x+3)dy+f1''y2dx+xyf1''dy+yf2''dx+3yf2''dy =(f1''y2+yf2'')dx+[f(xy,x+3y)+xyf1''+3yf2'']dy 即: ? z/? x=f1''y2+yf2'', ? z/? y=f(xy,x+3y)+xyf1''+3yf2'', ...