Free Printable Calculus

1.

dy/dx = 2x/e^2y find the general solution

a)

$y=\frac{\ln\left(2x^2+2C\right)}{2}$

b)

$y=\ln\left(2x^2+2C\right)$

c)

y = e^2x+c

d)

y = mx+b

2.

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

a)

𝑦 = ln(15t)

b)

𝑦 = 16t³

c)

𝑦 = (2𝑡³− 16)^1/2

d)

𝑦 = (2𝑡³−16)

3.

$\frac{dy}{dx}=\frac{\sqrt[]{y}}{x}$

Find the general solution

a)

√y = ln|4x| + c

b)

√y = (x)^-1 + c

c)

2y^1/2= ln|x| + c

d)

1/2y^1/2= ln|x| + c

4.

what would the sign of the square root after finding c be given the initial condition g(1)= -5

a)

positive

b)

negative

5.

dy/dx = (4x)^-1find the general solution

a)

y= 1/5x^5/4 + c

b)

y= 1/4ln|x| + c

c)

y= 1/8x² + c

d)

y= 1 + c

4x

6.

dy/dx = 4x/y. Suppose y(0)=1

The particular solution is

a)

B

b)

C

c)

D

d)

E

7.

Find the "C" if $\frac{dy}{dx}=2x\cdot\sqrt[]{y}$ and y = 4 when x = 3.

a)

2

b)

-5

c)

-2

d)

4

8.

∫dx

a)

x+c

b)

2x+c

c)

3x+c

d)

4x+c

9.

Find the mistake if possible:

a)

The Diff EQ is solved correctly

b)

Step 1 is incorrect. The separation of variables wasn't done correctly.

c)

Step 2 is incorrect. They didn't integrate x² correctly.

d)

Step 3 is incorrect. They didn't take the reciprocal of x³/3+C correctly.

10.

Find the Particular Solution

a)

$y=2+e^{\left(\frac{x^2}{2}+x\right)}$

b)

$y=2e^{\left(\frac{x^2}{2}+x\right)}$

c)

$y=\ln\left|\frac{x^2}{2}+x+1\right|+2$

d)

$y=\ln\left|\frac{x^2}{2}+x+e^2\right|$

11.

Determine the value of "c" that satisfies the differential equation $\frac{dy}{dx}=\frac{x+1}{y+2}$ if the curve goes through the point (0, -1).

a)

5/2

b)

-3/2

c)

-1/2

d)

1

12.

Which of the following is the solution to the differential equation $\frac{dy}{dx}=\frac{x^2}{y}$ with the initial condition y(3) = -2?

a)

$y=-2e^{\left(-9+\frac{x^3}{3}\right)}$

b)

$y=\sqrt{\frac{2x^3}{3}}$

c)

$y=\sqrt{\frac{2x^3}{3}-14}$

d)

$y=-\sqrt{\frac{2x^3}{3}-14}$

13.

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)

$\sin y=0+C$

14.

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

a)

$1=e^x+C$

b)

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

c)

$y=e^x+C$

d)

$0=e^x+C$

15.

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

a)

$y=e^{3x+C}$

b)

$y=3x+C$

c)

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

d)

$\ln y=x+C$

Calculus - Diff EQs

Total questions: 15

Worksheet time: 30mins

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