求(y x)通解dy (x-y)dx=0的
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∵(x+y)dy+(x-y)dx=0==>(1+y/x)dy+(1-y/x)dx=0设y=xt,则dy=tdx+xdt∴(x+y)dy+(x-y)dx=0==>(1+t)(tdx+xdt)+(1-t)
分离变量法dy/y=(1+x)dx,两边积分,得ln|y|=x+x平方/2+C,整理得y=Ce的(x+x平方/2)方
dy/dx=(x+y)/(x-y)x+y=u,x-y=ty=(u-t)/2x=(u+t)/2dy/dx=(du+dt)/(du-dt)=u/tudu-udt=tdu+tdtudu-tdt=udt+td
特征方程r+1=0r=-1通解y=Ce^(-x)设特解y=axe^(-x)y'=ae^(-x)-axe^(-x)代入原方程得ae^(-x)-axe^(-x)+axe^(-x)=e^(-x)解得a=1因
令y/x=py=pxy'=p+p'x代入原方程得p+p'x=p+xp'x=xp'=1两边积分得p=x+Cy/x=x+C
dy/dx+y/x=cosx积分因子=e^∫1/xdx=e^ln|x|=x,乘以方程两边x·dy/dx+y=xcosxd(xy)/dx=xcosxxy=∫xcosxdxxy=∫xd(sinx)=xsi
dy/dx=-x/yydy=-xdx两边积分y²/2=-x²/2+Cy²=-2x²+Cy²+2x²=C再问:有错吧亲。y²/2=-
x^2y''-2xy'=y'^2-(2xy'-x^2y'')/y'^2=1(x^2/y')'=-1两边积分:x^2/y'=-x+C1y'=x^2/(-x+C1)=(x^2-C1x+C1x-C1^2+C
∵dy/dx=sin(x-y)==>dy=sin(x-y)dx==>dx-dy=dx-sin(x-y)dx==>d(x-y)=(1-sin(x-y))dx==>d(x-y)/(1-sin(x-y))=
∵(y^2+xy^2)dx+(x^2-yx^2)dy=0==>y²(1+x)dx+x²(1-y)dy=0==>[(y-1)/y²]dy=[(1+x)/x²]dx
将方程写为dx/dy=1-x/y解齐次方程得x=C/y再用系数变易法求得一个特解为x=y/2 所以通解为x=C/y+y/2
dy/dx=(x+y)²令t=x+y,dt/dx=1+dy/dxdt/dx-1=t²dt/dx=(1+t²)dt/(1+t²)=dxarctan(t)=x+C&
令u=10^(x+y)则y=lnu/ln10-xy'=u'/(uln10)-1代入原方程:u'/(uln10)-1=udu/[u(u+1)]=ln10dxdu[1/u-1/(u+1)]=ln10dx积
通除y^3套公式解得y^-2=.
(dy/dx)-y=e^xdy-ydx=e^xdxdy=(y+e^x)dxdy=d(xy+e^x)y=xy+e^x+Cy=e^x/(1-x)+C
1、y'+y=x是一阶非齐次线性微分方程,通解是有专门公式的,套用,得y=Ce^(-x)+x-12、y'=-2/3x^(-5/3),x=1时,y'=-2/3,此为切线的斜率x=1时,y=1,所以切点是
求dy/dx=(x/y)+cos²(x/y)通解令x/y=u,则y=x/u,dy/dx=[u-x(du/dx)]/u²,代入原式得:[u-x(du/dx)]/u²=u+c