Free Printable Differential eqns daily work

1.

Solve the following differential equation.

$\frac{dy}{dx}=y^2$

a)

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

b)

$\frac{1}{y}=x+C$

c)

$-\frac{1}{y}=x+C$

d)

$y^3=x+C$

2.

Given the following differential equation and the initial condition, determine the constant of integration (C) of the solution.
$\frac{dy}{dx}=2y$ (1, 1)

a)

C = -1

b)

C = 2

c)

C = -2

d)

C = 1

3.

Solve the following differential equation.

$\frac{dy}{dx}=\frac{3x}{y}$

a)

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

b)

$y^2=x^2+C$

c)

$y=x+C$

d)

$y^2=x+C$

4.

Solve the following differential equation.

$y'=\frac{x+1}{\sin y}$

a)

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

b)

$\sin y=x^2-x+C$

c)

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

d)

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

5.

Solve the following differential equation.

$\frac{dy}{dt}=\frac{\sec^2t}{\sqrt{y}}$

a)

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

b)

$\frac{2}{3}y^{-\frac{3}{2}}=3\tan t+C$

c)

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

d)

$\sqrt{y}=\tan t+C$

6.

Solve the following differential equation.

$\frac{dy}{dx}=\frac{-7}{5xy}$

a)

$\frac{5y^2}{2}=-7x+C$

b)

$\frac{5y^2}{2}=-7\ln\left|x\right|+C$

c)

$5y^2=\ln\left|x\right|+C$

d)

$5y^2=-7x+C$

7.

Given the following differential equation and the initial condition, determine the constant of integration (C) of the solution.
$y'=6x^5$ (1, -2)

a)

C = -1

b)

C = 3

c)

C = -3

d)

C = 1

8.

Given the following differential equation and the initial condition, determine the constant of integration (C) of the solution.
$y'=6x^5$ (1, -2)

a)

C = -1

b)

C = 3

c)

C = -3

d)

C = 1

9.

Given the following differential equation and the initial condition, determine the constant of integration (C) of the solution.
$\frac{dy}{dx}=-\cos x$ $\left(\pi,\ 0\right)$

a)

C = 0

b)

C = 1

c)

C = 2

d)

C = 3

10.

Given the following differential equation and the initial condition, determine the constant of integration (C) of the solution.
$\frac{dy}{dx}=\frac{2x}{\sin y}$ $\left(2,\ 0\right)$

a)

C = -5

b)

C = 5

c)

C = 0

d)

C = 3

Differential eqns daily work

Total questions: 10

Worksheet time: 2hrs 40mins

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