2x+y=dy/dx求高手解答谢谢.

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/10/02 16:25:02

2x+y=dy/dx
求高手解答谢谢.

∵y=Ce^x(C是常数)是齐次方程y=dy/dx的通解
∴设原方程的解为y=C(x)e^x (C(x)是关于x的函数)
∵y'=C'(x)e^x+C(x)e^x,代入原方程得
C'(x)e^x=2x
==>C'(x)=2xe^(-x)
==>C(x)=∫2xe^(-x)dx=C-2(x+1)e^(-x) (C是常数)
∴y=C(x)e^x=Ce^x-2(x+1)
故原方程的通解是y=Ce^x-2(x+1).

2x+y=dy/dx求高手解答谢谢. 求dy/dx=(x-y+5)/(x+y-2) 求dy/dx=x/y+(cosx/y)^2通解 (x^2)dy+（y^2)dx=dx-dy y=2x^2+x求dy/dx x=sin(y/x)+e^2 求dy/dx y=e^x/x^2+sin2x 求dy/dx Y=2-sinx.求dy/dx及dy/dx|x=0 dy/dx=-x/y 求通解求dy/dx= - x/y y=(sinx)^x 求DY/DX y=x+lnx,求dx/dy