1.dy/dx=(xy^2-cosxsinx)/(y(1-x^2)),y(0)=2求y
举一反三
- 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: \( y'' + xy' = 4{x^2} + 1 \)
- <img src="http://edu-image.nosdn.127.net/E6A0628104FCB0F521FBF2AAAC7F1968.png?imageView&thumbnail=890x0&quality=100" style="width: 558px; height: 33px;" />? syms xy=log(1/x*x+exp(x))+sin(1-x^2)dy/dx=diff(y,x)|syms xy=log(1/x/x+exp(x))+sin(1-x^2)dydx=diff(y,x)|syms xy=log(1/x/x+exp(x))+sin(1-x)^2dydx=diff(y,x)|syms xy=log(1/x/x+exp^x)+sin(1-x^2)dydx=diff(y,x)
- 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: $y={{C}_{1}}{{e}^{{{C}_{2}}x}}$
- 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: \(\left( { { x^2} - y} \right)dx - xdy = 0\)
- 急设x=2t^(2)-1,y=根号(1+t^2).求dy/dx和d^2y/dx^2