求下列微分方程的通解,xdy/dx=(yIn^2)y,[(y+1)^2]dy/dx+x^3=0,dy/dx=2^(x+y),6x+y
1.求xdy/dx=yIn²y通解∵xdy/dx=yIn²y==>dy/(yIn²y)=dx/x==>d(lny)/In²y=dx/x==>-1/lny=ln│x│+C(C是积分常数)经检验y=1也是原方程的解∴原方程的通解是y=1或-1/lny=ln│x│+C(C是积分常数)...
举一反三
- 下列方程中,不是全微分方程的为( )。 A: \(\left( {3{x^2} + 6x{y^2}} \right)dx + \left( {6{x^2}y + 4{y^2}} \right)dy = 0\) B: \({e^y}dx + \left( {x \cdot {e^y} - 2y} \right)dy = 0\) C: \(y\left( {x - 2y} \right)dx - {x^2}dy = 0\) D: \(\left( { { x^2} - y} \right)dx - xdy = 0\)
- 函数\(z = {x^y}\)的全微分为 A: \(dz = y{x^{y - 1}}dy + {x^y}\ln xdx\) B: \(dz = y{x^{y - 1}}dx + {x^y}dy\) C: \(dz = y{x^{y - 1}}dx + {x^y}\ln xdy\) D: \(dz = y{x^{y - 1}}dy + {x^y}dx\)
- 一阶微分方程dy/dx=xcos(x^2)/y
- 设函数y=y(x)由方程2^xy=x+y所确定,则dy|x=0=() A: (ln2-1)dx B: (l-ln2)dx C: (ln2-2)dx D: ln2dx
- 下列方程中( )是一阶线性微分方程。 A: \( 2{x^2}yy' = {y^2} + 1 \) B: \( xy' + {y \over x} - x = 0 \) C: \( \cos y + x\sin y { { dy} \over {dx}} = 0 \) D: \( y'' + xy' = 4{x^2} + 1 \)
内容
- 0
求微分方程x(1+y2)dx=y(1+x2)dy的通解.
- 1
求方程$y\frac{{{d}^{2}}y}{d{{x}^{2}}}-(\frac{dy}{dx})^{2}=0$的通解: A: $y={{C}_{1}}{{e}^{-{{C}_{2}}x}}$ B: $y={{C}_{1}}{{e}^{-{{C}_{2}}{{x}^{2}}}}$ C: $y={{C}_{1}}x{{e}^{-{{C}_{2}}{{x}^{2}}}}$ D: $y={{C}_{1}}{{e}^{{{C}_{2}}x}}$
- 2
形如( )的方程,称为可分离变量方程,这里\(f(x), g(y)\)分别为\(x, y\)的连续函数。 A: \(\frac{dy}{dx}=f(x)g(y)\) B: \(\frac{dy}{dx}=f(x)\) C: \(\frac{dy}{dx}=f(x)+g(y)\) D: \(\frac{dy}{dx}=\frac{f(x)}{g(y)}\)
- 3
急设x=2t^(2)-1,y=根号(1+t^2).求dy/dx和d^2y/dx^2
- 4
求函数的导数dy/dx,和微分dy:y=x√1-x