Consider the initial value problem below. The value of y at x=\ln 2, (rounded off to 3 decimal places) is \frac{d y}{d x}=2 x-y, y(0)=1

Correct Answer is : 0.88 - 0.8863

GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 16 of 65

Marks: +1, -0

Consider the initial value problem below. The value of

y

x=\ln 2

, (rounded off to 3 decimal places) is

\;{d y}/{d x}=2 x-y, \;\; y(0)=1

Solution:

\;{d y}/{d x}+y=2 x

This is linear first order differential equation.
Integrating factor

=e^{∫ 1 {dx}}=e^{ {x}}

Solution is given as

y e^{x}=∫ e^{x} 2 x d x+c

y e^{x}=2[x e^{x}-e^{x}]+c

y=2(x-1)+c e^{-x}

{x}=0, {y}=1

{c}=3

y=2(x-1)+3 e^{-x}

x=\ln 2

, then

y=

y=2(\ln 2-1)+3 e^{-\ln 2}

y=2(\ln 2-1)+\;{3}/{2}

y=-0.6137+1.5=0.886

Go to Question:

Prev Question

Next Question