答案;得通解 x^3-2y^3=Cx 。 解析;原方程可写 (x^2/y^2+y/x)dx/3-dy=0 令u=y/x,即y=xu,有 dy= udx+ xdu,则原方程发为 (1/u^2+u)dx/3-(udx+xdu)=0 (3u^2)/(1-2u^3)du=1/xdx 积分得 -ln|1-2u^3V_2=ln|x|+lnC_1 ,即 1-2u^3=C(1)/C_1^2x^2) 将u=...
1 利用观察法求出下列方程的积分因子, 并求其通解: (1)(x+y)(dx-dy)=dx+dy; (2)ydx-xdy+y2xdx=0; (3)y2(x-3y)dx+(1-3y2x)dy=0; (4)xdx+ydy=(x2+y2)dx; (5)(x-y2)dx+2xydy=0; (6)2ydx-3xy2dx-xdy=0. 2 利用观察法求出下列方程的积分因子, 并求其通解: (1)(...
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(3)xdy+ydx=e^xydx 扫码下载作业帮搜索答疑一搜即得 答案解析 查看更多优质解析 解答一 举报 (1)(xy+x^3y)dy-(1+y^2)dx=0 (xy+x^3y)dy=(1+y^2)dx 分离变量整理得:y\(1+y^2)dy=1\x(1+x^2)dx 整理:y\(1+y^2)dy=1\x-x\(1+x^2)dx两边同时积分得1\2ln(1+y^2)=lnx-1\...
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3.求下列微分方程的通解.(1) 3y'-5x^2+2x=1 ;(2) y'-xy=0 ;(3) (1-x)y'=a(y^2-y^1) ;(4) xdy=√(1-y^2)dx ;(5) sec^2xtanydy+sec^2ytanxdx=0 ;(6) ydx+(x^2-4x)dy=0 ;(7) y'(e^(x+y)+e^y=e^(x+y)-e^x ;(8) x^2y'-lnx=0 ;(9) ...
结果一 题目 xdy+ydx=(x^3y^2-x)dx 答案 将左端改写成d(xy) 左端改写成x(x𠆢2y𠆢2-1)dx移项成d(xy)/(x𠆢2y𠆢2-1)=xdx将u=xy 右端成du/(u𠆢2-1) 两边积分 得(ln丨u-1丨-ln丨u十1丨)/2=x𠆢2/2+C得到解的隐函数形式...相关推荐 1xdy+ydx=(x^3y^2-x)dx ...
Discussed in #33509 Originally posted by akil-rails May 21, 2023 Hi How can I figure out the source/reason for the error ERROR [io.ver.cor.net.imp.ConnectionBase] (vert.x-eventloop-thread-0) invalid version format: <!DOCTYPE. I see this ...
(-5) , (du)/(dx)=-5y^(-6)=-5y-6(dy)/(dx) 原方程化为 (du)/(dx)-5⋅u/x=-5 x2.对应的齐次方程为dx(du)/(dx)-(5u)/x=0,分离变量解得 u=cx^5 ,将常数变量即令 u=x^5⋅c(x) 代人(du)/(dx)-5u/x=-5x^2 得 c'(x)x^5+5x^4c(x)-5c(x)x^5...
(4) (√2)/2=C∴cosy=(√2)/2cosx解:x/(1+y)dx=y/(1+x)dy 1+y1+x∫(y+y^2)dy=∫(x+x^2)dx (y^2)/2+(y^3)/3=x/2+(x^3)/3+C 由y()=1,有 1/2+1/3=C , C=5/62y3x2x2523236即 3y^2+2y^3=3x^2+2x^3+5解: ∫sin2ydy=∫(e^x-1)dx-1/2cos2y...