Differential equation 1 marks

 GATE 2019 Set-1 

1. For the equation \(\large \frac{\mathrm{d} y}{\mathrm{d} x}+7x^{2}y=0\),if \(y\left ( 0 \right )=\frac{3}{7}\), then the value of 𝑦(1) is

(A) (7/3)𝑒−7/3 

(B)  (7/3)𝑒−3/7

(C)  (3/7)𝑒−7/3 

(D)  (3/7)𝑒−3/7

Answer

 GATE 2019 Set-2 

1. The differential equation dy/dx + 4= 5 is valid in the domain 0 ≤ x ≤ 1 with (0) = 2.25 . The solution of the differential equation is

(A) = e – 4+ 5

(B) = e – 4+ 1.25

(C) y= e 4+ 5

(D) y= e 4+ 1.25

Answer

 GATE 2018 Set-2 

1. Consider a function u which depends on position x and time t. The partial differential equation

\(\large \frac{\partial u}{\partial t}=\frac{\partial^2 u}{\partial x^2}\)

is known as the

(A) Wave equation

(B) Heat equation

(C) Laplace’s equation

(D) Elasticity equation

Answer

2. If y is the solution of the differential equation \(y^{3}\frac{\mathrm{d} y}{\mathrm{d} x}+x^{3}=0, y\left ( 0 \right )=1\) , the value of \(y\left ( -1 \right )\) is

(A) −2

(B) −1

(C) 0

(D) 1

Answer

 GATE 2017 Set-1 

1. Consider the following partial differential equation for u(x,y) with the constat c > 1 :
\(\large \frac{\partial u}{\partial y}+c\frac{\partial u}{\partial x}=0\)

Solution of this equation is

(A) u (x,y) = f (x+cy)

(B) u (x,y) = f (x-cy)

(C) u (x,y) = f (cx+y)

(D) u (x,y) = f (cx-y)

Answer

2. The differential equation \(\large \frac{\mathrm{d} ^2y}{\mathrm{d} x^2}+16y=0\) for y(x) with the two boundary conditions \(\large \frac{\mathrm{d} y}{\mathrm{d} x}\mid _{x=0}=1\) and \(\large \frac{\mathrm{d} y}{\mathrm{d} x}\mid _{x=\frac{\pi}{2}}=-1\) has

(A) no solution

(B)exactly two solutions

(C) exactly one solution

(D)infinitely many solutions

Answer

 GATE 2014 Set-4 

1. The solution of the initial value problem \(\large \frac{\mathrm{d} y}{\mathrm{d} x}=-2xy;y(0)=2\) is

(A)\(\large 1+2e^{-x^2}\)

(B)\(\large 2e^{-x^2}\)

(C)\(\large 1+e^{x^2}\)

(D)\(\large 2e^{x^2}\)

Answer

 GATE 2013 

1. The partial differential equation \(\large\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=\frac{\partial^2 u}{\partial x^2}\) is a

(A) linear equation of order 2

(B) non-linear equation of order 1

(C) linear equation of order 1

(D) non-linear equation of order 2

Answer

 GATE 2010 

1.The Blasius equation,\(\large \frac{\mathrm{d}^3f }{\mathrm{d} \eta^3}+\frac{f}{2}\frac{\mathrm{d}^2f }{\mathrm{d} \eta^2}=0\), is a

(A) second order nonlinear ordinary differential equation

(B) third order nonlinear ordinary differential equation

(C) third order linear ordinary differential equation

(D) mixed order nonlinear ordinary differential equation

Answer

 GATE 2008 

1. Given that \(\large \ddot{x}+3x=0\), and \(\large x(0)=1,\dot{x}(0)=0\), what is \(\large x(1)\)?

(A) -0.99

(B) -0.16

(C) 0.16

(D) 0.99

Answer

 GATE 2007 

1. The partial differential equation \(\large \frac{\partial^2 \varphi}{\partial x^2}+\frac{\partial^2 \varphi}{\partial y^2}+\frac{\partial \varphi}{\partial x}+\frac{\partial \varphi}{\partial y}=0\) has

(A) degree 1 order 2

(B) degree 1 order 1

(C) degree 2 order 1

(D) degree 2  order 2

Answer

 GATE 2006 
1. The solution of the differential equation \(\large \frac{\mathrm{d} y}{\mathrm{d} x}+2xy=e^{-x^2}\) with y(0)=1 is:

(A) \(\large (1+x)e^{+x^2}\)

(B) \(\large (1+x)e^{-x^2}\)

(C) \(\large (1-x)e^{+x^2}\)

(D) \(\large (1-x)e^{-x^2}\)

Answer

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