[y+√(x²+y²)]dx=xdy满足y(1)=0的解
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/26 02:21:58
![[y+√(x²+y²)]dx=xdy满足y(1)=0的解](/uploads/image/z/11967552-0-2.jpg?t=%5By%2B%E2%88%9A%EF%BC%88x%26sup2%3B%2By%26sup2%3B%EF%BC%89%5Ddx%3Dxdy%E6%BB%A1%E8%B6%B3y%EF%BC%881%EF%BC%89%3D0%E7%9A%84%E8%A7%A3)
[y+√(x²+y²)]dx=xdy满足y(1)=0的解
[y+√(x²+y²)]dx=xdy满足y(1)=0的解
[y+√(x²+y²)]dx=xdy满足y(1)=0的解
[y+√(x²+y²)]dx=xdy满足y(1)=0的解
dy/dx=[y+√(x²+y²)]/x=y/x+√[1+(y/x)²].(1)
令y/x=u,则y=ux,dy/dx=u+x(du/dx),代入(1)式得:u+x(du/dx)=u+√(1+u²),消去u即得:
x(du/dx)=√(1+u²),分离变量得:du/√(1+u²)=(dx)/x
积分之,得 ln[u+√(1+u²)]=lnx+lnC=ln(Cx)
故有u+√(1+u²)=Cx,将u=y/x代入即得:
y/x+√[1+(y/x)²]=Cx,于是得通解 y+√(x²+y²)=Cx²
将初始条件:x=1时y=0代入,即得C=1,故得特解为 y=x²-√(x²+y²)
x²-y²-x-y因式分解
6xy²-9x²y-y²因式分解
49+14x+x²-y²
因式分解 (x²+y²-1)²-4x²y²
求因式分解:(x²+y²)²-4x²y²
(x²+y²)²-4x²y² 因式分解
因式分解:x²-11x²y²+(y²)²
(x²+4y²)²-16x²y² 因式分解
分解因式:(x²+y²)²-4x²y²
分解公因式(X²+y²)²-x²y²
已知(x²+y²)(x²+y²-6)+9=0 ,求x²+y²的值.
若x²+xy-2y²=0,则x²+3xy+y²/x²+y²
x²+xy-2y²=0则x²+3xy+y²/x²+y²
1/√(x²+y²)的导数是多少
(x+y)²-2(x²-y²)+(y-x)²
9(x-y)²+12(x²-y²)+4(x+y)² 因式分解
已知(x+y)²;=8,(x-y)²;=4,求x²+y²
分解公因式 (x+y)²-2(x²-y²)+(x-y)²