xy’+x+sin(x+y)=0 求解该积分方程 .急.
来源:学生作业帮助网 编辑:作业帮 时间:2024/10/06 16:36:12
xy’+x+sin(x+y)=0 求解该积分方程 .急.
xy’+x+sin(x+y)=0 求解该积分方程 .
急.
xy’+x+sin(x+y)=0 求解该积分方程 .急.
∵xy’+x+sin(x+y)=0
==>x(y'+1)=-sin(x+y)
==>x(dy/dx+dx/dx)=-sin(x+y)
==>xd(x+y)/dx=-sin(x+y)
==>d(x+y)/sin(x+y)=-dx/x
==>sin(x+y)d(x+y)/sin²(x+y)=-dx/x
==>d[cos(x+y)]/[1-cos²(x+y)]=dx/x
==>{1/[1+cos(x+y)]+1/[1-cos(x+y)]}d[cos(x+y)]=2dx/x
==>ln[1+cos(x+y)]-ln[1-cos(x+y)]=2ln│x│+ln│C│ (C是积分常数)
==>[1+cos(x+y)]/[1-cos(x+y)]=Ce^(2x)
==>cos(x+y)=[Ce^(2x)-1]/[Ce^(2x)+1]
∴原方程的通解是cos(x+y)=[Ce^(2x)-1]/[Ce^(2x)+1] (C是积分常数).
xy’+x+sin(x+y)=0
令x+y=p
两边求导得
1+y'=p'
代入得
x(p'-1)+x+sinp=0
xp'+sinp=0
dp/sinp=-dx/x
两边积分得
-1/2ln(1+p)+1/2ln(1-p)=-lnx+C
xy’+x+sin(x+y)=0 求解该积分方程 .急.
求解微分方程xy'ln(x)sin(y)+cos(y)(1-x*cos(y))=0
sin(x+y)+e^xy=4 求y'
设函数f(x,y)=sin(x+y),那么f(0,xy)=( )
x^2-xy-2y^2=0是怎么变成(x+y)(x-2y)=0求解,
sin(x*x+y)=xy 求y'x
用mathematica软件,求解三角函数方程组.形如:Solve[{Cos (x y) == 1,Sin (x y) == 0},{x,y}].为什么mathematica软件计算无解.(其实解为xy=Pi/2)
xy''-y'-x^2=0求解微分方程
sin(xy)=x+y,求dy
sin(xy)=x 求dx/dysec(xy)-y ]/x 还是 x/[sec(xy)-y]
求解微分方程(xy^2+x)dx+(y-x^2y)dy=0,y(2)=1的通解
求解常微分方程 xy(y-xy')=x+yy',y(0)=(1/2)*根号2
sin(x+y)+e^xy=4x,y'=
sin(xy)+ln(y-x)=x,求y`
sin(xy)+ln(y-x)=x,求y
求解微分方程y'*cos(y)=x+1-sin(y)
微分方程xy''=y'-x(y')^2的通解为 y''+2y'=0求解,
求解12x²-10xy+2y²+11x-5y+2=0