7 Show that y 8. -7x is a solution of the differential equation y' + 7y = y = -7x + e y' = y' + 7y = + 7 · 8 LHS = RHS, %3D

Q: 2. Show that y = e-6t satisfies the differential equation y" – y – 42y = 0.

A: We have to verify that y''-y'-42y=0 when y=e-6t. We know that d2ydt2=y''dydt=y'de-atdt=-ae-at So…

Q: 5. For what values of r does the function y = e™* satisfy the differential equation 2y" + y' – y =…

A: Given , differential equation       2y" + y' - y = 0   (2D2 + D - 1)y = 0 The auxiliary equation of…

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y=ae +be¯ª.

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: (b) Form the differential equation by eliminating the arbitrary constants a,b from y = aez + be 8z

A: Differentiate twice with respect to x then we get the answer

Q: 3. Find the general solution y = Yc + Yp to the differential equation. Use the uppercase letters C…

A:

Q: The solution of Bernoulli Differential equation y'+-y=3y²; x>0 will be found after reducing it to…

A: Given, The bernoulli's equation y' + yx = 3y-2            x>0

Q: Find the general solution of the first-order linear differential equation. y + y = 16 cos (x)…

A:

Q: Obtain approximate value of y at x=1.5 for the differential equation: y'-2y+3ex, y(0)-1, using Runge…

A:

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: Suppose that y1 = e x and y2 = e −x are the solution of a homogenous linear differential…

A:

Q: The differential equation formed by eliminating arbitrary constants a and 6: y = ax + bx+9 is

A: Given that

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

A: Eliminating arbitrary constants a & b using derivatives.

Q: 2. Form the differential equation from the circle passing through the origin having their centers on…

A: This question is based on forming differential equation by eliminating constant.

Q: What is the particular solution to the 2² +3 with the differential equation dy da 3y initial…

A:

Q: Find the particular solution of differential equation = 4ye* using the given boundary condition: y =…

A: We have differential equations and both of them are variable separables.

Q: Determine an appropriate choice for a particular solution for the differential equation y" + 4y = 3…

A:

Q: 21. Find particular solution of the differential equation- 2(x + 1)³ = dx (x+1) Y , given x = 0,…

A:

Q: 2. Test the exactness and obtain the general solution of the differential equation: 2+yexy y' =…

A:

Q: Determine the values of r for which the differential equation y'-y = 0, has a solution of the y =…

A:

Q: The independent variable x is missing in the given differential equation. Proceed as in Example 2…

A: Given:y+8yιι =yι2   →1Let yι =u →Ad2ydx2=dydxd2ydx2=dudy=dydxd2ydx2= ududy →Busing Aand B in 1we…

Q: 2. Consider the differential equation y' -()y = 2+G) t If y(0) = yo, find the particular solution to…

A: Explanation of the solution is given below...

Q: Find the general solution for the second-order differential equation ¨y + 8 ˙y − 9y = −3 with…

A:

Q: int (1,7), given that  y = 2x2 + 3x + C is a general solution to the differential equation. Hint…

A: The differential equation given is, dydx=4x+3. Integrate the differential equation,…

Q: The actual solution to the differential equation y = 7 with the boundary condition y(0) = 8 is O y =…

A:

Q: Excrcise 1: 1. Let the following higher order differential equation (1) y/" – 2 y" – 3 y = 3e.…

A: For higher order differential equation,           Let  P0xyn +P1xyn-1+.........+Pnxy =F(x) .....(A)…

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

A:

Q: Let the following higher order differential equation y" – 2 y" – 3 y' = 3e5z (1). Determine the…

A: Consider the given information: y'''-2y''-3y'=3e5x To find the general solution by variation of…

Q: 2. What should be A for the exact differential equation of ry + A , 2Ay – 1 dr+ y? Moreover evaluate…

A:

Q: The differential equation y' – y = 0 has a solution of 1 y(x) = n! n=0 Show v(r) is a soluution to…

A:

Q: Eliminate the arbitrary constants in the equation defined by y = ae^(3x) + bxe^(3x). Which of the…

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: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

A:

Q: Consider the Non-Homogenous differential equation: y"-y= 6sinx Given that y. = Ce* + Cze-*, using…

A: Suppose we have second order linear differential equation as .  Consider are independent solutions…

Q: The solution of the first order linear differential equation y' + ycotx = cosx is O…

A:

Q: Show that y=x and yex are lenean inde pendent Solution of the Corres pondinp hamogeneous part ot the…

A:

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

A: To Determine -

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

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: The Integrating Factor of the differential equation dy dr y = 14x? is x-14 25 e5z

A: The given differential equation is,  dydx-5xy=14x2To find its integrating factor.

Q: Determine the general solution of the given differential equation. y(4) + 2ylI + 2yl/ -x = 3e" + 2e™…

A:

Q: Obtain the general solution of the given Differential Equation using the Method of Variation of…

A:

Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

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: he of the curves corresponding to different values of C in the general solution of the differential…

A:

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

A:

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