Q. 175.0( 1 Vote )

Show that the equation of the curve whose slope at any point is equal to y + 2x and which passes through the origin is y + 2(x + 1) = 2e2x.

Answer :

Given slope at any point = y + 2x



We can see that it is a linear differential equation.


Comparing it with


P = – 1, Q = 2x


I.F = e∫Pdx


= e – dx


= e – x


Solution of the given equation is given by


y × I.F = ∫Q × I.F dx + c


y × e – x = ∫ 2x × e – x dx + c


ye – x = 2∫ x × e – x dx + c


ye – x = – 2x e – x – 2 e – x + c


y = – 2x – 2 + cex ……(1)


As the equation passing through origin,


0 = 0 – 2 + c× 1


c = 2


Putting the value of c in equation (1)


y = – 2x – 2 + 2ex


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