Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy2 2.13 + x²y +y³ b. (e"cos(x))y' = x4 + 6x²y³ y +vx³ C. y' = cos(5) %3D x+x2

Q: 1. 2. (√ex + (ex)³) dx /22sinx cos x dx

A:

Q: Find dy/dx for each of the following. Do not simplify your answers. 3 (a) y = 3* – 3x7 + cot(3x³ +…

A: Part(a) Given

Q: 8. Show that the function y = ex (sin 2x + cos 2x) is a solution of the equation y" — 2y' + 5y = 0.

A: The given function is; y=ex(sin2x+cos2x) And the given equation is; y''-2y'+5y=0.

Q: 4. (6 points) Using separation of variables, solve the differ- ential equation, (1+7)dy dx y Use C…

A:

Q: h45. Solve for the general solution of y'= sinx + ycotx a. y = (x+ C)sinx b. y = Cxsinx c. y = (x +…

A:

Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: 37/2 8 cos x dx T/2

A:

Q: (3x² – 2xy+ y²) dx + (2xy – x² + sin y) dy = 0, y(12) = 0 - |

A: We have to find the required solution of…

Q: ion C(x)=10x+700 are produced. Find the  fixed co

A:

Q: 4- Determine an expression for dy/dx. 3(y-2)3– x= 4x - 6.

A:

Q: Ex6: Solve the following 1. If x? + y² = 25 show that (y')² + yy" + 1 = 0 2. If xy = sin x show that…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral.

Q: 3. Integrate the function. (a) / Vx–1dx = %3D (b) /e2+ 2x+1 dx = (c) | (sin xcosx+ sinx cos x) dx =…

A: Hello there! You seem to have uploaded a question with multiple subparts. As per our guidelines, we…

Q: S(6Vx + 3 cos x - 8)dx

A:

Q: Find dy/dx.  Y3 + (y+2)2 - 1 - x2 = x

A: Expand the left hand side expression and isolate the variables x and y.…

Q: B) Find (dy/dx) for the following 1. y = tan2(cosx)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Solve (yz + хуz) dx + (zx + хуz) dy + (ху + хуz) dz =

A:

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx b.…

A: Separable equation:   A first order differential equation y’ = f (x, y) is called a separable…

Q: Find the dx/dy of 2x² + 4y² = 4.

A:

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

A:

Q: dy Q1/ Find dx 1. if y = u and u 4x2-2x +5. %3D 2. y = (x2 + 4)2(2x3- 1)3 %3D 3. xy + x- 2y- 1 = 0…

A:

Q: IV. 4x + 2 dx x² + x + 5 V. 2x – 1 dx x² – 7x + 10 VI. | sin(3x) cos(5x) dr

A:

Q: 5. (x + y)dy – (x – y)dx = 0. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: find dy/dx of the following:

A: Please refer to the image below

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.