We have the linear differential equation
xux+yuy=u
The system of eqautions is,
xdx=ydy=udu
Now, taking first two terms
xdx=ydy
Integrating Both the sides-
lnx=lny+C1lnx−lny=lneC1
(yx)=eC1yx=C1′ϕ=yx=C1′
Now, taking last two terms
⇒ydy=udu⇒lny=lnu+C2⇒lny=lnu+lneC2⇒ln(uy)=lneC2
⇒uy=eC2
⇒uy=C2′
⇒ϵ=uy=C2′
Hence, the general solution is f(ϕ,ϵ)=f(yx,uy)=0
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Dear Opeyemi Yahaya, please use the panel for submitting a new question.
Solve (d²u)/(dxdt) = sin(x+t) at t=0, ux=1 and at x=0, x=(1-t)²
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