y(2xy+e^(x))^(x)dx-e^(x)dy=0 (e ^ (y) +1) cos xdx + e ^ (y) sin xdy = 0 The solution ofy(2xy+ex)dx−exdy=0is (A)x2+ye−x=C(B)xy2+e−x=C(C)xy+e−xx2=C(D)x2+exy=C View Solution The solution of ex(y2−1)y{xy2dy+y3dx}+{ydx−xdy}=0...
G(y)=(1/P)(∂P/∂y-∂Q/∂x)={1/[y(xy+1)]}(2xy+2)=2/y;故得积分因子μ(y)=e^∫(-2/y)dy=1/e^(2lny)=1/e^(lny²)=1/y²;把原方程的两边乘上这个积分因子,得一全微分方程:(x+1/y)dx-(x/y²)dy=0,即有d(x²/2+x/y)=0故得原方程的通解为:x²/2+...
下列微分方程:(1) (3x^2y+2xy+y^3)dx+(x^2+y^2)dy=0 ;(2) ydx+(2xy-e^(-2y))dy=0 ;(3) (3x+6/y)dx+((x^2)/y+(3y)/x)dy=0 ;6(5) 2xy^3dx+(x^2y^2-1)dy=0(6)y(1+xy)dx -xdy =0;(7) y^3dx+2(x^2-xy^2)dy=0 ;(8)e^xdx+(e^x)coty+2...
解微分方程(xy²+y)dx-xdy=0 解：先求积分因子：P=xy²+y，Q=-x；∂P/∂y=2xy+1；∂Q/∂x=-1；G(y)=(1/P)(∂P/∂y-∂Q/∂x)={1/[y(xy+1)]}(2xy+2)=2/y；故得积分因子μ(y)=e^∫(-2/y)dy=1/e^(...
解：∵y²dx+(y²+2xy-x)dy=0 ==>e^(1/y)*y²dx+e^(1/y)*(y²+2xy-x)dy=0 (方程两端同乘e^(1/y))==>e^(1/y)*y²dx+e^(1/y)*(2y-1)xdy+e^(1/y)*y²dy=0==>e^(1/y)*y²dx+xd[e^(1/y)*y²]+e^(1/...
Answer to: Solve the following linear differential equations. 1. 2 \frac{dy}{dx} - y = e^\frac {x}{2} \\ 2. xdy + ydx = \sin x dx By signing up,...
xy'-ylny=0 ;(e^y)/(1+e^y)d=(2x)/(1+x^2)dx ;3. 1/(y+3)dy=2xdx ;4. y'=(1+y^2)/(xy+x^2y);xy+x3y5. (1+x)ydx+(1-y)xdy=0;6. y'=e^(x-y) ;7. x(y^2-1)dx+y(x^2-1)dy=0 ;8. y'=(1+x^2)(1+y^2) ;9. y'=2xy,y|_(x=0...
5.求下列微分方程的通解:(1) y'-2xy=e^(x^2)cosx ;(2) y'+ysinx=sin^3 x;(3) (y+x^2e^(-x))dx-xdy=0 ;(4) (sin^2y+xcoly)y'=1 ;5)y^2dx+(x-2xy-y^2)dy=0 ;(6) y'+y/x=y^2lnx ;(7) 2y'sinx+ycosx=y^3(xcosx-sinx) . ...
解题过程如下：D(XY) = E{[XY-E(XY)]^2} = E{X²Y²-2XYE(XY)+E²(XY)} = E(X²)E(Y²)-2E²(X)E²(Y)+E²(X)E²(Y)= E(X²)E(Y²)-E²(X)E²(Y)如果 E(X) = E(Y) = 0,那么 ...
{eq}y'' - y = e^x {/eq} Non-homogeneous Differential Equation: If the right-hand side of any differential equation is non-zero, it is known as a non-homogeneous differential equation. The complete solution of the non-homogeneous differential equation is the sum of complementary function an...