please solve dy/dx-2y/x=e^1/x

Solve dy/dx-2y/x=e^1/x
in Algebra 1 Answers by Level 12 User (101k points)

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14 Answers

X→1/t and dy/dx→-t^2 dy/dt
by Level 12 User (101k points)
The givenis transformed into (2ty+e^)dt+t^2dy=0
by Level 12 User (101k points)
P_=2ty+e^t
by Level 12 User (101k points)
Q_=t^2
by Level 12 User (101k points)
æp/æy=æq/æx so (1) is exact
by Level 12 User (101k points)
du_=Pdt+Qdy=0
by Level 12 User (101k points)
→ u(y,t)=c
by Level 12 User (101k points)
æu/æy=Q
by Level 12 User (101k points)
→u=t^2y+w(t)
by Level 12 User (101k points)
æu/æt=p_=2ty+w'(t)
by Level 12 User (101k points)
→ w(t)=e^t
by Level 12 User (101k points)
(2),(3)→u_=t^2y+e^t
by Level 12 User (101k points)
Y(t)=1/t^2 (c!-e^t)
by Level 12 User (101k points)
t→1/x: y(x)=x^2(c-e^1/x)
by Level 12 User (101k points)

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