==>(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)/3=C/3 (C是积分常数)
==>3x^2y+y^3=Ce^(-3x)
∴此方程的通解是3x^2y+y^3=Ce^(-3x)。
求微分方程 (3x^2y+2xy+y^3)dx+(x^2+y^2)dy=0
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问一道微分方程问题,请问这个全微分求解是怎么做的?
是用了积的微分法则，d(uv)=udv+vdu，两个括号里面的项分别凑出了乘积的形式。
求微分方程 y(x^2-xy+ y^2)dx+ x(x^2 +xy+ y^2)dy=0 的通解
如图中：
求微分方程通解求微分方程(3x^2+2xy-y^2)dx+(x^2-xy)dy=0的通解.?
∵(3x²+2xy-y²)dx+(x²-xy)dy=90 同除以x^2 (3+2y\/x-(y\/x)^2)dx+(1-y\/x)dy=0 y\/x=u y=ux y'=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...
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(x^2y+y)dy + (xy^2+x)dx = 0 是全微分方程， 通解是 ∫<0, x> (xy^2+x)dx + ∫<0, y> (0^2y+y)dy = C\/2 即 x^2y^2 + x^2 + y^2 = C
求微分方程y^2dx+(x^2-xy)dy=0 的通解
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...
...2x)dx+2ydy=0 麻烦给出过程,答案为:x+ln(x^2+y^2)=C
解答过程如下：(x^2+y^2+2x)dx+2ydy=0 (x^2+y^2)dx+d(x^2)+d(y^2)=0 (x^2+y^2)dx+d(x^2+y^2)=0 x+ln(x^2+y^2)=C
求微分方程(x+xy^2)dx-(x^2y+y)dy=0的通解,谢谢
2011-03-28 求(x+xy^2)dx-(x^2y+y)dy=0的通解!~ 2017-06-23 求微分方程(y+xy^2)dx+(x-x^2y)dy=0的通... 8 2016-06-07 求微分方程的通解 (x-2y)dy+dx=0 16 2016-04-29 求(xy^2-x)dx +(x^2y y)dy=0的通解 2 2015-04-16 大学数学求通解 (y+xy^2)dx+(x-x^2y)...
微分方程y^3dx+2(x^3-xy^2)dy=0的通解为多少
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...
求微分方程通解 求微分方程xdx+(x^2*y+y^3+y)dy=0的通解
变形：(xdx＋ydy)＋y(x^2+y^2)dy＝0,以1\/(x^2+y^2)为积分因子,得 (xdx＋ydy)\/(x^2+y^2)＋ydy＝0 d[ln(x^2+y^2)＋y^2]＝0 所以通解是 ln(x^2+y^2)＋y^2＝C
