Integrate the following expression, and solve for the constant of integration using the fact that y =-19 when a= 2. 2/3 +11 dy = -4x dx Answer is y as a function of x (include the value of C in your answer): y =

Q: ex dx /1-ex

A: Integration means addition it is used for adding continuous function which can't be added by simple…

Q: C. e3x dx

A: Given- ∫01e3xdx To Find- The value of the above definite integral.

Q: Solve this differenttial equation.   By help of integrating factor. (3xy+6y^2).dx+(2x^2+9xy).dy=0

A:

Q: Which constant c would best be described as a constant of integration? c +1 Secx=a

A: The indefinite integral always results a constant of integration.

Q: Verify the exactness of the given function (1+ex/y)dx+ex/y(1-x/y)dy=0 and then write the complete…

A: Solution: The objective is to find the general solution of the given differential equation

Q: I. Evaluate the following and show all necessary solutions. Enclose your final answer. dx (x2 + 1)3…

A:

Q: d) fe'cos( 41)

A:

Q: e-SP(x) dx x²(x) as instructed, to find a second solution y₂(x). 6y"+y¹ - y = 0; Y₁ = ex/³ Y₂ 11 Y₂…

A: Given DE is  6y"+y'-y=0 .......(1) Also given y1=ex/3. We find y2(x).

Q: Choose the correct answer for the following integration e2 dx 2х (In x)3 (A) e (B) -3 (C) (D) 8. (E)…

A: Given integral,

Q: Q2. (b) Given that y =. a sin(ln x) solves r²y" – xy + 2y = 0, determine the general solution.

A:

Q: x(2y – 3)dx + (x2 + 1)dy = 0

A:

Q: Solve the following equation and find the solution y as a function of x and C (constant of…

A: We have observed that the given differential equation is a first order separable ODE. So, by…

Q: Q1: Find dy/dx for the following functions (solve four only):-

A:

Q: x dx 1) S 1-2x

A: As there are multiple questions, 1)  is solved here.

Q: dx J (5 + x5)2

A:

Q: 4. (ху + 1)dх +x?dy 3D 0

A: The differential equation is given as (xy+1) dx+x2 dy=0. We need to solve the equation by…

Q: + (3x + 1)y = e d« dx

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: x2 +1 3. xe dy + dx = 0

A:

Q: Try this: Solve the following DE. 1. (x2 + y2)dx + x(x- 2y)dy = 0

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: cos a eT dx ¤ dx Csc x

A:

Q: I. Differentiate implicitly to find 1. x3 +y3 10 dx xp %3D 2. x2 + y? = 25 %3D 3. x3 y5 %3D

A: Disclaimer: Since you have posted a question with multiple subparts, we will solve the first three…

Q: A. Solve the following equation using integrating factors found by inspection. 5. x(x? - y? - x)dx –…

A: Given differential equation is: x(x2-y2-x)dx-y(x2-y2)dy=0 To solve the equation using integrating…

Q: / 2x/64 – x* dx Evaluate the integration by substitution 16л 4л

A:

Q: Q1: Use Picard's method to solve - = 2x - 3y, y(1)=2 up to third approximation and use it dx find…

A: Given dydx=2x3-3y, y(1)=2to find the value of y (1.5) by picards methid upto 3rd approximator.

Q: Q/ Solve the differential equetion (x²4)dy=zxy dx

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as…

Q: Solve the following using exact equation or linear whichever is applicable. (x− 2y)dx + (y − x) dy=…

A: Given: (x− 2y)dx + (y − x) dy= 0

Q: B: Solve the following integrations: a- fx³e-2x dx b-fdx +10 c-f 3sec³x. tanx dx

A:

Q: S2(x* +1)e** dx . -5x t³ -9 -dt . 2t +3

A:

Q: r1.25 x2 dx with h=0.25. 1+x3 Using numerical methods find the value of

A:

Q: Solve the given IVP. x²° = y² + xy y(1) = 1 %3D dx Hint: Use substitution to change the equation to…

A:

Q: 2. y(2x – y + 1)dx + x(3x – 4y + 3)dy = 0

A:

Q: Solve the following DE V2+ x? dy =-x 1+y dx y = Ce{2+x²) _ 1 а. y= Ceor") _1 y = Ce{2+x?)

A:

Q: 3x 2. S dx Jx2-x-2

A:

Q: (x - 3y)dr – rdy =0

A: The given first order differential equation is Simplify the given equation

Q: integration faed dx dx

A: we have to calculate integration

Q: Solve the following separable DEs, writing your solution as in explicit function y = y(x) if…

A:

Q: Solve the derrivative and enclose the final answer. xdy - { y + xy3 (1 + ln x) } dx = 0

A:

Q: The equation below follows from the integration by parts formula by replacing u by  f(x)  and v by a…

A: Recall the following fact.

Q: 99. (2ry'e +2ry+y)dz+(z*y*e® -z'y-3z)dy= 0

A: Solution :                              (1) The given differential equation is(2xy4ey+2xy3+y) dx+…

Q: B: Solve the following integrations: a- fx³e-2x¹ dx b-fdx c-f 3sec³ x. tanx dx marks

A:

Q: Solve the first ODE and find the value of C constant when v(1)-2 dy 6x2 + 4x + 4 dx 4y

A:

Q: (z- 2y)dr+ ydy = 0 %3D

A:

Q: 5 3t2 (t3 + 4)°dt

A: