Ordinary Differential Equations

Q.

The solution of the differential equation x dx + y dy = 0 is:

1. xy = c, where c is any constant.

2. y = cx, where c is any constant.

3. x = cy, where c is any constant.

4. x + y = c, where c is any constant.

Q. The kind of differential equations in which dependent variables depend on one independent variable is called ordinary differential equations

1. True
2. False

Q. How many arbitrary constants are there in the general solution of the differential equation of order 3.

Q.

What is the difference between derivative and differential?

Q. What is the general form of first order linear differential equation in x ?

Q.

The first order linear differential equation, where y is independent and x is dependent variable, is:

1. 

2. 

3. 

4. 

Q. 49.The solutions of p+cos(px)sin(y)= sin(px)cos(y) ( where p= dy/dx) Options a)y=0 b) cx-y=arcsin(x) c)cx-y= arcsin(c) d)y=(x-1 )-arcsin((x-1)/x)

Q.

What is the maximum and minimum value of cos(cosx)

Q. Let $f:[1,\infty )\to [2,\infty )$ be a differentiable function such that $f\left(1\right)=2.$ If $6{\int }_1^{x}f\left(t\right)dt=3xf\left(x\right)-x^3\text{for all}x\ge 1,$ then the value of $f\left(2\right)$ is

Q.

Why we add c while doing integration .can u explain me with the help of an example

Q. If the worlds population is growing at the rate of 1.1% per year. Approximately how long will it take for it to double? (ln 2 = 0.69)

1. 25 years
2. 97 years
3. 63 years
4. 127 years

Q. Find the order of differential equation whose general solution is given by y=(k_1+ k_2)tan(x+k_3)-k_4e^x+k_5 where k_1k_2 k_3k_4 k_5 are arbitrary constants.

Q. Solution of differential equation (1+x)(1+y^2)dx+(1+y)(1+x^2)dy=0 is

Q.

The general solution of the differential equation is

A. xy = C

B. x = Cy²

C. y = Cx

D. y = Cx²

Q. Are parameters and arbitrary constants same in terms of differential equation ?

Q. 30. The solution of differential equation Xdy/dx = -y/2-sin2x/2y is

Q. The general solution of the differential equation $\frac{dy}{dx}=e^{x+y}$, is
(a) e^x + e^−y = C
(b) e^x + e^y = C
(c) e^−x + e^y = C
(d) e^−x + e^−y = C

Q. $y=x+\mathrm{sinx}\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{which}\mathrm{of}\mathrm{these}\mathrm{differential}\mathrm{equations}?$

1. $\frac{\mathrm{dy}}{\mathrm{dx}}=1+\mathrm{cosx}$
2. $\frac{d^{2}y}{{\mathrm{dx}}^2}+\mathrm{sinx}=0$
3. $\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{cosx}$
4. $\frac{d^{2}y}{{\mathrm{dx}}^2}-\mathrm{sinx}=0$

Q. If y=y(x) is the solution of the differential equation, xdy÷dx+2y=x^2 satisfying y(1)=1, they(1÷2) is equal to

Q. (xe^x/y +y)dx = (x) dy
Solve the differential equation!

Q.

Find a particular solution of the differential equation , given that y = 0 when

Q. Identify ordinary differential equations

1. $\frac{dy}{dx}+\frac{dz}{dx}=y+z$
2. $\frac{dy}{dx}+x^{2}y=\sec x$
3. $(\frac{dy}{dx}{)}^2=\ln \left(y\right)$
4. $\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}=x$

Q. The number of solutions for inequality |2^x-1|+|4-2^x|<3 are

Q. solve differential equation 2 dy/dx = y/x +( y/x)²

Q. solve the differential equation x sec^2y dy = (x\ln x + 1)e^xdx

Q.

The differential equation for the equation y = Acos αx + Bsin αx is:

1. 

2. 

3. 

4. 

Q.

The solution of differential equation x²dy + y(x + y)dx = 0 when x = 1, y = 1 is:

1. 

2. 

3. 

4. 

Q. If $y=100+f\left(x\right)$ is the particular solution of differential equation $\frac{dy}{dx}=100-y$ and $y\left(0\right)=50,$ then the value of $f\left(1\right)$ is

1. $50e$
   
2. $-50e$
3. $-\frac{50}{e}$
4. $\frac{50}{e}$

Q. Show that y = C x + 2C² is a solution of the differential equation $2{\left(\frac{dy}{dx}\right)}^2+x\frac{dy}{dx}-y=0$.

Q.

Show that the general solution of the differential equation is given by (x + y + 1) = A (1 – x – y – 2xy), where A is parameter