Free Printable Differential Equation (Separable Variable)

1.

The following Differential Equation is
$\frac{\text{d}y}{\text{d}x}=\frac{y}{x}$

a)

Separable.

b)

Non Separable

2.

The following Differential Equation is
$\frac{\text{d}y}{\text{d}x}=x^2y+x$

a)

Separable.

b)

Non Separable.

3.

The following Differential Equation is
$x\frac{\text{d}y}{\text{d}x}=yx^2$

a)

Separable.

b)

Non Separable.

4.

The following Differential Equation is
$\frac{\text{d}y}{\text{d}x}=y^2+xy^2$

a)

Separable.

b)

Non Separable.

5.

The following Differential Equation is
$\frac{\text{d}y}{\text{d}x}=\frac{e^y}{e^x}$

a)

Separable.

b)

Non Separable.

6.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=\frac{y}{x}$

a)

$y=Ax$

b)

$y^2=\ln x+C$

c)

$\ln y=\frac{x^2}{2}+C$

d)

$A=yx$

7.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=\frac{1}{\cos y}$

a)

$\sin y=1+C$

b)

$\sin y=x+C$

c)

$-\sin y=\frac{x^2}{2}+C$

d)

$\sin y=0+C$

8.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=3y$

a)

$y=Ce^{3x}$

b)

$y=3x+C$

c)

$\frac{y^2}{2}=3x+C$

d)

$\ln y=x+C$

9.

Solve the equation

$\frac{dx}{dt}=3xt^2$

a)

$x=e^{t^3}+\ C$

b)

$x=Ce+t^3$

c)

$x=Ce^{t^3}$

d)

$x=e^t+3C$

10.

Solve the initial value problem

$y'=x^3\left(1-y\right)\ \ \ \ ,\ \ \ \ \ \ y\left(0\right)=3$

a)

$y=e^{-x^4}+8$

b)

$y=2e^{\frac{-x^4}{4}}+1$

c)

$y=\frac{-x^4}{4}+C$

d)

$y=e\frac{-x^4}{2}+1$

Differential Equation (Separable Variable)

Total questions: 10

Worksheet time: 5mins

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