y′′-2y′-3y=(x-1)e∧x的通解
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原式=(9x²+24xy+16y²-4x²+y²-5x²+6xy-y²)÷(-2y)=(30xy+16y²)÷(-2y)=-15x
由2(X+Y)3X+3Y=24得:2(X+Y)X+Y=8①;(X+Y/2X)XY/2Y=1得:X+Y=4②;由①、②得出Y=8(1-X),进入②知X=4/7;即Y=24/7
y'=-x/ydy/dx=-x/yydy=-xdxy²/2+C1=-x²/2+C2化简可得:y²+x²+C=0y=√(-x²+C)
选C分离变量得:(1/y)dy=(2/x)dx两端取积分得:ln|y|=2ln|x|+c(c为任意性常数)即ln|y|=ln(x^2)+lnc(c和lnc是一个概念)(c为任意性常数)即|y|=cx^
(1)令y/x=t,则y=tx,dy=xdt+tdx原方程化为:xdt/dx+t=t+tlntxdt/dx=tlntdt/(tlnt)=dx/x两边积分:ln|lnt|=ln|x|+Clnt=Cx(C
(x+2)(x+3)=x²+5x+6(x-4)(x+1)=x²-3x-4(y+4)(y-2)=y²+2y-8(y-5)(y-3)=y²-8y+15x²
已知x-y=1,则y=x-1,x=y+1{(x+2y)²+(2x+y)(x+4y)-3(x+y)(x-y)}÷y=(x²+4xy+4y²+2x²+9xy+4y&
微分方程y″-2y′-3y=3x+1+ex的特征方程为:λ2-2λ-3=0,求解可得其特征值为:λ1=-1,λ2=3.对于微分方程y″-2y′-3y=3x+1,①由于0不是方程的特征根,故其特解形式为
1)x(x-y)(x+y)-x(x+y)^2=x((x-y)(x+y)-(x+y)^2)=x(x^2-y^2-x^2-2xy-y^2)=x(-2xy-2y^2)=-2xy(x+y)2)(2a+b)(2
[(-x-y)(-x+y)-(x+y)^2-x(y-y^2)}÷1/2y=[x²-y²-x²-2xy-y²-xy+xy²]/(y/2)=[(x-2)y
(x+1)y'-2y=(x+1)^4(x+1)dy/dx-2y=(x+1)^4dx=d(x+1)(x+1)dy/d(x+1)-2y=(x+1)^4(x+1)dy-2yd(x+1)=(x+1)^4d(x
解(x-y)(x+y)-(x-2y)²+x(3x-5y)-(x-y)(x-2y)=(x²-y²)-(x²-4xy+4y²)+(3x²-5xy
1/(x-y)-1/(x+y)-2y/(x^2+y^2)-4y^3/(x^4+y^4)-8y^7/(x^8+y^8)=【(x+y)-(x-y)】/(x-y)(x+y)-2y/(x^2+y^2)-4y^
3(x+y)-4(x-y)=4(x+y)/2+(x-y)/6=1令a=x+y,b=x-y3a-4b=4(1)a/2+b/6=1则3a+b=6(2)(2)-(1)5b=2b=2/5a=(6-b)/3=2
1、(-7x^y)(2x^y-3xy^3+xy)=-14x^(2y)+21x^(y+1)y^3-7x^(y+1)y;2、((x-y)^6)/((y-x)^3)/(x-y)=-(x-y)^3/(x-y)
y*=b0xe^x,y*'=b0(e^x加xe^x),y*''=b0(2e^x加xe^x)代入解得:b0=-2
设一个变量u=y/x,带入方程很好求解,解不出来再联系我哈
y=e^2x+x^2-yarcsin(1/x)y'=2e^2x+2x-y'arcsin(1/x)+y1/[x^2*√(1-1/x^2)]y'={2e^2x+2x+y1/[x^2*√(1-1/x^2)]