Differential Equation Practice Questions – Mathematics

#13080Objective

Determine the order and degree of the differential equation \(2x\frac{d^4y}{dx^4}+5x^2(\frac{dy}{dx})^3-xy=0\)

AFourth order, first degree

BThird order, first degree

CFirst order, fourth degree

DFirst order, third degree

#13081Objective

Which of the following equations is an exact DE?

A\((x^2+1)dx-xy\,dy=0\)

B\(x\,dy+(3x-2y)dx=0\)

C\(2xy\,dx+(2+x^2)dy=0\)

D\(x^2y\,dy-y\,dx=0\)

#13082Objective

Which of the following equations is a variable separable DE?

A\((x+x^2y)dy=(2x+xy^2)dx\)

B\((x+y)dx-2y\,dy=0\)

C\(2y\,dx=(x^2+1)dy\)

D\(y^2dx+(2x-3y)dy=0\)

#13083📜 ECE Board April 1998Problem

The equation \(y^2=cx\) is the general solution of:

A\(y'=\frac{2y}{x}\)

B\(y'=\frac{2x}{y}\)

C\(y'=\frac{y}{2x}\)

D\(y'=\frac{x}{2y}\)

#13084📜 EE Board March 1998Problem

Solve the differential equation: \(x(y-1)dx+(x+1)dy=0\). If \(y=2\) when \(x=1\), determine \(y\) when \(x=2\).

A1.80

B1.48

C1.55

D1.63

#13085📜 EE Board October 1997Problem

If \(dy=x^2 dx\); what is the equation of \(y\) in terms of \(x\) if the curve passes through \((1,1)\)?

A\(x^3-3y+3=0\)

B\(x^3-3y+2=0\)

C\(x^3+3y^2+2=0\)

D\(2y+x^3+2=0\)

#13086📜 ECE Board November 1998Problem

Find the equation of the curve at every point of which the tangent line has a slope of \(2x\).

A\(x=-y^2+C\)

B\(y=-x^2+C\)

C\(y=x^2+C\)

D\(x=y^2+C\)

#13087📜 ECE Board April 1995Problem

Solve \((\cos x \cos y-\cot x)dx-\sin x \sin y\,dy=0\).

A\(\sin x \cos y=\ln(c \cos x)\)

B\(\sin x \cos y=\ln(c \sin x)\)

C\(\sin x \cos y=-\ln(c \sin x)\)

D\(\sin x \cos y=-\ln(c \cos x)\)

#13088📜 EE Board October 1997Problem

Solve the differential equation \(dy-x\,dx=0\), if the curve passes through \((1,0)\)?

A\(3x^2+2y-3=0\)

B\(2y+x^2-1=0\)

C\(x^2-2y-1=0\)

D\(2x^2+2y-2=0\)

#13089📜 ME Board April 1996Problem

What is the solution of the first order differential equation \(y(k+1)=y(k)+5\)?

A\(y(k)=4-\frac{5}{k}\)

B\(y(k)=20+5k\)

C\(y(k)=C-k\), where C is constant

DThe solution is non-existent for real values of y

#13090📜 EE Board April 1995Problem

Solve \((y-\sqrt{x^2+y^2})dx-x\,dy=0\).

A\(\sqrt{x^2+y^2}+y=C\)

B\(\sqrt{x^2+y^2+y}=C\)

C\(\sqrt{x+y}+y=C\)

D\(\sqrt{x^2-y}+y=C\)

#13091📜 ECE Board November 1994Problem

Find the differential equation whose general solution is \(y=C_1 x + C_2 e^x\).

A\((x-1)y''-xy'+y=0\)

B\((x+1)y''-xy'+y=0\)

C\((x-1)y''+xy'+y=0\)

D\((x+1)y''+xy'+y=0\)

#13092📜 EE Board October 1995Problem

Find the general solution of \(y'=y \sec x\).

A\(y=C(\sec x+\tan x)\)

B\(y=C(\sec x-\tan x)\)

C\(y=C \sec x \tan x\)

D\(y=C(\sec^2 x \tan x)\)

#13093📜 EE Board April 1996Problem

Solve \(xy'(2y-1)=y(1-x)\).

A\(\ln(xy)=2(x-y)+C\)

B\(\ln(xy)=x-2y+C\)

C\(\ln(xy)=2y-x+C\)

D\(\ln(xy)=x+2y+C\)

#13094📜 EE Board April 1996Problem

Solve \((x+y)dy=(x-y)dx\).

A\(x^2+y^2=C\)

B\(x^2+2xy+y^2=C\)

C\(x^2-2xy-y^2=C\)

D\(x^2-2xy+y^2=C\)

#13095Problem

Solve the linear equation: \(\frac{dy}{dx}+\frac{y}{x}=x^2\).

A\(xy^2=\frac{x^3}{4}+C\)

B\(xy=\frac{x^4}{4}+C\)

C\(x^2y=\frac{x^4}{4}+C\)

D\(y=\frac{x^3}{4}+C\)

#13096📜 CE Board May 1997Problem

Find the differential equations of the family of lines passing through the origin.

A\(y\,dx-x\,dy=0\)

B\(x\,dy-y\,dx=0\)

C\(x\,dx+y\,dy=0\)

D\(y\,dx+x\,dy=0\)

#13097📜 CE Board May 1996Problem

What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis.

A\(2x\,dy-y\,dx=0\)

B\(x\,dy+y\,dx=0\)

C\(2y\,dx-x\,dy=0\)

D\(\frac{dy}{dx}-x=0\)

#13098📜 CE Board November 1995Problem

Determine the differential equation of the family of lines passing through \((h,k)\).

A\((y-k)dx-(x-h)dy=0\)

B\((y-h)+(y-k)=\frac{dy}{dx}\)

C\((x-h)dx-(y-k)dy=0\)

D\((x+h)dx-(y-k)dy=0\)

#13099Problem

Determine the differential equation of the family of circles with center on the y-axis.

A\((y'')^3-xy''+y'=0\)

B\(y''-xyy'=0\)

C\(xy''-(y')^3-y'=0\)

D\((y')^3+(y'')^2+xy=0\)