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(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) ...

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...

(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...

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:∵(3x^2y+2xy+y^3)dx+(x^2+y^2)dy=0 ==>(3x^2ydx+2xydx+x^2dy)+(y^3dx+y^2dy)=0 ==>(3x^2ye^(3x)dx+2xye^(3x)dx+x^2e^(3x)dy)+(y^3e^(3x)dx+y^2e^(3x)dy)=0 (等式两端同乘e^(3x)) ==>d(x^2ye^(3x))+d(y^3e^(3x))/3=0 ==>x^2ye^(3x)+y^3e^(3x)...

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。

最后两排怎么变得cx

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(...

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