Questions
If y = y(x) is the solution of the differential equation, , such that y(0) = 0, then y(1) is equal to:
a
2e
b
2+loge2
c
1+loge2
d
loge2
detailed solution
Correct option is C
The given differential equation is eydydx-1=ex ⇒ey-xdydx-1=1Substitute y-x=tDifferentiate w.r.t. x both sidesdydx-1=dtdxThe given differential equation becomes etdtdx=1etdt=dx ⇒∫etdt=∫dx⇒et=x+c ⇒ey-x=x+cSubstitute x=0 y=0 given y(0)=0 it gives c=1Hence the solution is ey-x=x+1put x=1 to get the value of y1⇒ey-1=2 ⇒y-1=loge2 ⇒y=1+loge2=y(1)Talk to our academic expert!
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The general solution of the differential equation is
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