Free Printable DIFFERENTIAL EQUATIONS (MMR w3)

1.

Which of the following is a separable differential equation?

a)

$\frac{\text{d}u}{\text{d}t}+\frac{2u}{t}=8$

b)

$\frac{\text{d}y}{\text{d}x}-6x^2y=9x^2$

c)

$xy'-2y-x^3\cos x=0$

d)

$\frac{d\theta}{dt}+2\theta=\sin\ t$

2.

Solve the differential equation

\frac{dy}{dx}+2=2y

.

a)

$y=1+\sqrt{\frac{4}{-2x-A}}$

b)

$y=\frac{\beta e^x+2}{2}$

c)

$y=1+\alpha e^{2x}$

d)

$y=1+\frac{1}{-4x-A}$

3.

Find the general solution of the differential equation

2y\ dy-\left(y^2+1\right)\cos x\ dx=0

a)

$y=\sqrt{Ae^{\left(\sin x-1\right)}}$

b)

$y=\sqrt{Ae^{\sin x}-1}$

c)

$y=\sqrt{\frac{A}{e^{\sin x}}-1}$

d)

$y=\sqrt{\sin x-1}$

4.

If

y=\frac{e^{\left(\alpha x+\beta\right)}}{\gamma}

is the solution for differential equation

\frac{dy}{dx}=6y

, find the values of

\alpha,

\beta

and

\gamma

when

y=1,\ x=2

.

a)

$\alpha=1,\ \beta=0,\ \gamma=6$

b)

$\alpha=6,\ \beta=12,\ \gamma=6$

c)

$\alpha=12,\ \beta=6,\ \gamma=6$

d)

$\alpha=6,\ \ \beta=-12,\ \gamma=1$

5.

If the gradient of a curve is given as

\frac{1}{x^2y}

, find the equation of the curve at point

\left(2,3\right)

.

a)

$y=\sqrt{\frac{10x-2}{x}}$

b)

$y=\sqrt{9-\ln16-\frac{2}{x}}$

c)

$y=\sqrt{-\frac{1}{x}+\frac{19}{2}}$

6.

Which of the following differential equation CAN NOT be separated?

a)

$\frac{dy}{dx}+1=4x$

b)

$y^2\frac{dy}{dx}=\sqrt{xy}-2x^2\sqrt{y}$

c)

$\frac{dy}{dx}+\frac{2}{x}y=\frac{1}{x+1}$

d)

$\frac{dy}{dx}-e^xy=e^x$

7.

Do you think Week 3 questions are hard?

a)

Yes

b)

No

8.

Given the curve $Ax^2\ +\ y^2=B$ is the solution of the differential equations $\frac{dy}{dx}=-\ \frac{x}{y}$ , at $\left(2,0\right)$ . Find the values of $A$ and $B.$

a)

$A=\frac{1}{2},\ B=\frac{1}{4}$

b)

$A=\frac{1}{2},\ B=1$

c)

$A=1,\ B=4$

d)

$A=-1,\ B=4$

9.

Find the general solution for the differential equation $\frac{dy}{dx}=xy$ .

a)

$y=e^{\frac{x^2}{2}}+c$

b)

$y=\alpha e^{\frac{x^2}{2}}$

c)

$y=Ae^{x^2}$

d)

$y=\sqrt{\frac{1}{x^2+A}}$

10.

Given that the acceleration of an object satisfies the differential equation $e^t\frac{dv}{dt}=2\sqrt{v}$ . Find the equation of the velocity of the object if it started at $v=1.$

a)

$v=\left(2-e^{-t}\right)^2$

b)

$v=\left(3-2e^{-t}\right)^2$

c)

$v=\left(2e^{-t}-1\right)^2$

11.

Given the differential equation $\frac{dP}{dt}=5P$

A) Find the general solution for P .

B)Find the particular solution for P to the differential equation given $P\left(0\right)=418$ .

a)

A) $P=e^{5\alpha t}$
B) $P=e^{418t}$

b)

A) $P=\alpha e^{5t}$
B) $P=418e^{5t}$

c)

A) $P=\beta e^t$
B) $P=418e^t$

d)

A) $P=\alpha e^{10t}$
B) $P=418e^{10t}$

DIFFERENTIAL EQUATIONS (MMR w3)

Total questions: 11

Worksheet time: 8mins

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