Mathematics, 20.01.2020 23:31 jpdvolleybal8260

In each of problems 1 through 6, determine the order of the given differential equation; alsostate whether the equation is linear or nonlinear.(1) t^2 (d^2y/dt^2)+ t(dy/dt)+ 2y = sin t(2) (1 + y^2)(d^2y/dt^2)+ t(dy/dt)+ y = e^t(3) (d^4y/dt^4)+(d^3y/dt^3)+(d^2y/dt^2) +(dy/dt)+ y =1(4) (dy/dt)+ ty^2 = 0(5) (d^2y/dt^2)+ sin(t + y) = sin t

Answers: 3

Show answers

Answers

Answer from: denarreiahspen5921

The question is in complete, below is the complete question

"In each of Problems 1 through 6, determine the order of the given differential equation; also state whether the equation is linear or nonlinear

1. $t^{2}\frac{d^{2}y}{dt^{2}} +t\frac{dy}{dt}+2y=sint\\$

2. $(1+y^{2} )\frac{d^{2}y}{dt^{2}}+t\frac{dy}{dt}+y=e^{t} \\$

3. $\frac{d^{4}y }{dt^{4}}+ \frac{d^{3}y }{dt^{3}}+ \frac{d^{2}y }{dt^{2}}+ \frac{dy}{dt}+y=1$

4. $\frac{dy}{dt}+ty^{2}=0$

5. $\frac{d^{2}y }{dt^{2}}+sin(t+y)=sint$

6. $\frac{d^{3}y }{dt^{3}}+t\frac{dy }{dt}+cos^{2}(t)y=t^{3}$

below is the answer

1. second order, linear

2. second order, non- linear

3. fourth order, linear

4. first order, non- linear

5.second order, non- linear

6. third order, linear

Step-by-step explanation:

To determine the order of a differential equation, we look out for the highest derivative in the equation. if the power of the highest derivative is one, we call it a first order differential equation and if the highest power of the derivative is 2 we call it a second order differential equation.

Also a differential equation is said to be linear if the independent variable and its derivative are linear.

Now let use the above condition to check the following

1. $t^{2}\frac{d^{2}y}{dt^{2}} +t\frac{dy}{dt}+2y=sint\\$

the highest power of the derivative is 2 and the independent variable and its derivatives are linear hence we conclude second order, linear

2. $(1+y^{2} )\frac{d^{2}y}{dt^{2}}+t\frac{dy}{dt}+y=e^{t} \\$

the highest power of the derivative is 2 and the $y^{2}\frac{d^{2}y}{dt^{2}}$ is non-linear hence we conclude second order, non- linear

3. $\frac{d^{4}y }{dt^{4}}+ \frac{d^{3}y }{dt^{3}}+ \frac{d^{2}y }{dt^{2}}+ \frac{dy}{dt}+y=1$

the highest power of the derivative is 4 and the independent variable and its derivatives are linear hence we conclude fourth order, linear

4. $\frac{dy}{dt}+ty^{2}=0$

the highest power of the derivative is 1 and the $y^{2}$ is non-linear hence we conclude first order, non- linear

5. $\frac{d^{2}y }{dt^{2}}+sin(t+y)=sint$

the highest power of the derivative is 2 and the (t+y) is non-linear hence we conclude second order, non- linear

6. $\frac{d^{3}y }{dt^{3}}+t\frac{dy }{dt}+cos^{2}(t)y=t^{3}$

the highest power of the derivative is 3 and the independent variable and its derivatives are linear hence we conclude third order, linear

Answer from: Quest

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation:

Answer from: Quest

tip $2.90

total $17.40

Another question on Mathematics

Mathematics, 21.06.2019 15:50

Fredrick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Click the arrows to advance or review slides. mapping carbohydrates to food carbohydrates (grams) 15 food (quantity) bread (1 slice) pasta (1/3 cup) apple (1 medium) mashed potatoes (1/2 cup) broccoli (1/2 cup) carrots (1/2 cup) milk (1 cup) yogurt (6 oz.) 12 12 is jennifer's relation a function? yes no f 1 of 2 → jennifer figure out the difference between a function and a relation by answering the questions about her food choices

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

Solve the equation for x.3(6x - 1) = 12 i've tried doing the math and i can't find out what i'm doing wrong

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

Consider the first four terms of the sequence below. what is the 8th term of this sequence?

Answers: 1

Answer

You know the right answer?

In each of problems 1 through 6, determine the order of the given differential equation; alsostate...