www.ntzj.net > (x^2 3xy^2)Dx (3x^2y 2y^2)Dy=0求该全微分方程通解

(x^2 3xy^2)Dx (3x^2y 2y^2)Dy=0求该全微分方程通解

答案为x³/3 + 3x²y²/2 + 2y³/3 = C P = x² + 3xy²、P'y = 6xy Q = 3x²y + 2y²、Q'x = 6xy 所以是恰当方程。 令原函数为u(x,y) ∂u/∂x = x² + 3xy² u = ∫ (x² + 3xy²) ...

(x³+y³)dx-3xy²dy=0, 齐次方程的通解? 解:dy/dx=(x³+y³)/3xy²=(1/3)[(x/y)²+(y/x)]=(1/3)[1/(y/x)²+(y/x)] 令y/x=u,则y=ux,dy/dx=u+x(du/dx),代入上式得: u+x(du/dx)=(1/3)[(1/u²)+u] 故有x...

你确定没有题目没有抄错? 要是没有的话,以下是matlab的运算结果: >> clear >> syms x y >> dsolve('Dy=(2*x^3+3*x*y^2+x)/(3*x^2+2*y^3-y)') ans = (3^(1/2)*(- 2*x^2 - 1)^(1/2))/3 -(3^(1/2)*(- 2*x^2 - 1)^(1/2))/3 solve(12*x^2*y^2 - lo...

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=C。

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=C。

方程两端同乘y除x 然后代换xy的平方项 ……

x^3dx=3xy^2dy-y^3dx x^3dx=xdy^3-y^3dx xdx=dy^3/x+y^3d(1/x) 通解x^2/2=y^3/x+C

解:∵(3x²+2xy-y²)dx+(x²-xy)dy=90同除以x^2(3+2y/x-(y/x)^2)dx+(1-y/x)dy=0y/x=uy=uxy'=u'x+u(3+2u-u^2)+(1-u)(u'x+u)=0(3+2u-u^2)/(u-1)-u=u'x(3+2u-u^2-u^2+u)/(u-1)=u'x(-2u^2+3u+3)/(u-1)=u'x(u^2-1.5u-1.5)/(u-1)=-1/2u'x(...

此微分方程的通解为x^3-2y^2=C。 ∵(x^3+y^3)dx-3xy^2dy=0, ∴x^3dx=3xy^2dx-y^3dx, ∴xdx=[xd(y^3)-y^3dx]/x^2, ∴(1/2)d(x^2)=d(y^3/x), ∴(1/2)x^2=C+y^3/x, ∴x^3-2y^2=C。 ∴原微分方程的通解是:x^3-2y^2=C。...

1解: (x^2+y^2)dx-xydy=0;dy/dx=(x+y)/(xy);dy/dx=((x/y)+1)/(x/y); 令u=y/x,则dy=du*x+dx*u,dy/dx=(du/dx)*x+u, 代入得(du/dx)*x+u=(u+1)/u=u+1/u,du/dx=1/(xu),*du=dx/x, 两边积分得 (1/2)u=lnx+C 将u=y/x回代,(1/2)(y/x)=(lnx)+C...

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