求微分方程通解?
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(1)(1-a-x)y'=ay^2 dy/y^2=a/(1-a-x)dx -1/y=-ln[C(1-a-x) ] y=1/ln[C(1-a-x) ]
(3)ydx+(x^2-4x)dy=0 dy/y=-dx/(x^2-4x) lny=1/4∫[1/(x-4)-1/x]dx=1/4ln[C(1-4/x)]
y=[C(1-4/x)]^(1/4)
(5) xy'-ylny=0 dy/(ylny)=dx/x -1/(lny)^2=ln(CX) (lny)^2*ln(CX)=-1
(7) dy/dx=10^(x+y) dy/10^y=10^xdx -1/ln10*10^(-y)=1/ln10*10^x+C1 10^x+1/10^y=C,1,
(3)ydx+(x^2-4x)dy=0 dy/y=-dx/(x^2-4x) lny=1/4∫[1/(x-4)-1/x]dx=1/4ln[C(1-4/x)]
y=[C(1-4/x)]^(1/4)
(5) xy'-ylny=0 dy/(ylny)=dx/x -1/(lny)^2=ln(CX) (lny)^2*ln(CX)=-1
(7) dy/dx=10^(x+y) dy/10^y=10^xdx -1/ln10*10^(-y)=1/ln10*10^x+C1 10^x+1/10^y=C,1,
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