7. The differential equation which has y = C1r + C2x as its general solution is: 4 (a) y" – -y'+ y = 0 4. (b) y"+ -y' + (c) r²y" – 4ry' + 4y = 0 (d) r²y" – 2ry' + 4y = 0 (e) None of the above.

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: The brine is entering more and going out less at rate (3 gal/min -2 gal/min = 1 gal/min), so…

Q: 2. x²y' – 2xy = x* + 3; y = 2 when x = 1

A:

Q: 8. The differential equation (2x-xy-2y+3}dx-(x*y+2xkty = 0 is exact because ÔM ON

A:

Q: 2. What is the integrating factor of the differential equation (x² -y²)dx + (x² - 2xy)dy = 0?

A:

Q: Show that the first order differential equation (x + 1) y' - 3y = (x + 1)5 is of the linear type.…

A: To solve x+1y'-3y=x+15; y=1.5 when x=0

Q: 2 4 Solve the differential equation y dx - 2(y - x) dy = 0. If y = 1 when x = 3, determine x when y…

A:

Q: 4. Show that both x₁ (t) = et cost and x2(t) = et sint are solutions to the second-order…

A: To show that both x1t=e-t cos t, and  x2t=e-t sin tare solutions to the second‐order differential…

Q: What is the particular solution to the differential equation * + (1 + x)y = 12 with y 0 and = 0 when…

A: The solution is given as

Q: The general solution of the second-order differential equation y"-y-12y = 0 is: y = c₂e³x + c₂e-4x…

A:

Q: (4) a general solution of the 4th-order differential equation y +y(3) + y" = 0.

A:

Q: 1. Given the differential equation: y" = sin(5x). Determine its general solution. A. 150y = cos(5x)…

A: Given differntial equation          y'''=sin 5xthen we have to find it's general solution…

Q: 3. If the general solution to a second-order differential equation is given by cie + ce-5, find the…

A: In the question it is asked to solve the differential equations with initial values given.

Q: 5. By using separable differential equation, solve the initial-value problem 2x(y + 1)dx -y dy= 0,…

A:

Q: 2-The exact solution of differential equation ý--4y with y(0)-1 is (a) 2e-4x (b) e-4x (c) e-4x +1…

A: As per as our guideline i am supposed to answer only one question from all these question . To get…

Q: 1. Determine whether = is a solution of the differential equation y'--y = 0 3 y' = 6x² а. 6x2-…

A:

Q: 2. The differential equation (4x'y'-6x'y-2r-3)dr +(2x*y-2x' ty = 0 is exact because aN

A:

Q: 2. Prove that the given first order ordinary differential equation (2x – y) dx – (x – 2y) dy = 0 is…

A: A detailed solution is given below

Q: 5. The differential equation (3x'e' - 2xx+ (r'e' -sin y ldy = 0 is exact because ON

A: Partial differentiation is needed to be done after identifying M and N

Q: 2. What can you say about a solution of the equation y' = -25y2 just by looking at the differential…

A: Firstly we integrates, then solve it.

Q: 2. Form the differential equation from the family of curves y² = Ax² – Bx² , where A and B are…

A:

Q: Obtain the particular solution of (3x2-2y2)y'=2xy; when x=0. y=-1

A:

Q: Find the particular solution to the differential equation: dy = 3x² cos² y. sSolution passes through…

A: Differential calculus is one of two main parts of calculus which is concerned with the study of…

Q: y = - is one of the solutions to the non-homogeneous Cauchy-Euler equation 1 x²y" + xy' – y x + 1…

A:

Q: What is the general solution to the differential equation dydx=(x−1)/(3y^2) for y>0y>0

A:

Q: The General solution of differential equation def ined by: 2x² y " – x y'+y=0 is defined by y(x) =…

A: Solving Cauchy Euler differential equation

Q: For the differential equation (x2 – 4)y" + (x- 2)y' + 2y = 0, the singular points are: O None of…

A:

Q: The given differential equation is already in standard form, as the coefficient of the highest order…

A:

Q: 9. What is the particular solution of the linear differential equation ,3 Y = x° – 2xy; when x = 1,…

A:

Q: Suppose dr - =4sin(2x) and y= -2 when *=. what is the particular solution to the given differential…

A: In this question, we need to find the particular solution to the given differential equation.

Q: For the differential equation (x -4)y" + (x- 2)y'+ 2y 0, the singular points are: O None of them x-3…

A:

Q: 4. If the characteristic equation of the differential equation y"+2y'-3y =0 is m² + 2m –3 =0, then…

A:

Q: 4.Calculate the differential equation y''= 3x + y2 + y + y', y (0) = 2, y (1) = 4 by shoot-ing /…

A: Given that the differential equation is  y''=3x+y2+y+y'; y(0)=2, y(1)=4 Also given that h=1/3 we…

Q: on - Homogenous: To be considered Homogenous, the differential equation must be equal to ependent…

A: We are asked to find the  non homogeneous second order euqation.

Q: Determine the particular solution of the given differential equation: y = 2(3x +y) – 1. when x-0.…

A:

Q: 3. Given that y = 1 when x=-1, find particular solution to differential equation dx dy – 3x²y² =…

A:

Q: 5. (a) Find the particular solution of the differential equation x³ = 1-e²t if x(0) = 2.

A:

Q: The differential equation formed by eliminating arbitrary constants a ,b andc: y = ax + bx + cx + 8…

A: In this question, we have to find the differential equation by eliminating parameters.

Q: . Given the differential equation: y" = cos(5x). Determine its general solution. A. 125y = -cos(5x)+…

A:

Q: The solution of the differential equation by variable separable method dy (1+ y²) (3x² + 6) 5- is dx…

A:

Q: 8 Find the general solution of the differential equation: xy' + y: X Use lower case c for constant…

A: Given : xy'+y=8x+9x Following formulas are used- ∫1xdx=lnx∫xndx=xn+1  n+1

Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

A: Given:     Differential equation 2x3-xy2-2y+3dx-x2y+2xdy=0 The differential equation is exact if…

Q: Choose a solution for the differential equation y'' - y = x2ex + 5: e-x(1/6x3 - 1/4 x2 + 1/4x + 3)…

A: Given non- homogeneous differential equation,y''-y=x2ex+5  ...(1). Solving the homogeneous part:…

Q: 3. The differential equation = 8 – 2y can be solved using the method of separation of variables or…

A: solve using separation of variable dydt=8-2y dydt=-2y+8 dydt=-2y-4 dyy-4=-2dt take integration…

Q: y" – 2y' + y = -3 - x+x².

A:

Q: 3. ([3]) Suppose that a large mixing tank initially holds 400 gallons of water in which 50 pounds of…

A: This is a problem of IVP.

Q: 5. In the differential equation 2rydx + (y² -xy-0. what is -- 心

A: Solution

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = aeª +…

A:

Q: Find the general solution of the higher order linear ordinary differential equation: y"' + 2y" + 4'…

A: We have to find general solution of given differential equation.

Q: The given differential equation is already in standard form, as the coefficient of the highest order…

A: We have to find Wronskians.  Wronskian W(y1, y2) is the  W(y1, y2) = y1y2' − y2y1' Since y1 and y2…

Q: 7. Find the particular solution of the differential equation dx 5x³y = x³ passing through the point…

A: The given question has been solved in detail