6. Solve the initial-value problem y =-2xy', y(0)=1.

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: 2. Solve Bernoulli differential equation of y' + xy = xy².

A: We need to solve the differential equation.

Q: The general solution to a differential equation is given by y = c1e^(3x) + c2x. Suppose we then…

A: Solution:

Q: 1. Solve the linear differential equation of y' – 2xy = = X. swer:

A:

Q: find the solution of initial value problem. Using Differential Equations y'+2y=xe-2x,…

A:

Q: 3. What is the difference between a solution of a differentialequation and a solution of an…

A: The solution represents a family of solutions all of which satisfy the system of differential…

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

A: Given, dydx+5x3y=x3,   0,72 it is a linear differential equation p(x)=5x3,  q(x)=x3…

Q: 5. Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y )²

A: We have to evaluate: (y(x) + 1) ( d^2 y(x))/( dx^2) = (( dy(x))/( dx))^2:Treating y as the…

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

A:

Q: 4. Choose a solution to the differential equation y" + 3y' + 2y = sin eª.

A: Here we solve the differential equation using variation of parameter.

Q: Determine the solution to the differential equation given by: y'=6y2/x

A:

Q: Q5/: Find the general solution of non-homogenous differential equation using Variation of Parameters…

A:

Q: 3. Find the complete solution of the differential equation (4x + xy2) – (y – x?y)y' = 0 using…

A:

Q: ex 2. y" — 2у' + у %3 1+ x2

A:

Q: (9) Show that the solution of the differential equation y + y = -6ye» with y(0) = -1 is (e* –…

A:

Q: 2yy"=1+y'².

A: We have given differential equation ,  2yy'' = 1 + y'2 Here , substitute y' = u ⇒ y'' = u u'  Thus…

Q: If we use the method of variation of parameters, the particular solution of the following…

A: We have to assume the particular solution first.

Q: 5. Find the general solution of the differential equation y=(2y4+2x)y'.

A: Given differentiatial equation: y = (2y^4+2x)y'  Here y'= dy/dx

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

A:

Q: Determine the particular solution of the differential equation yi+yie(x/y}=+2x²e(z/y}? When y(0) = 1

A:

Q: If we use the method of variation of parameters, the particular solution of the following…

A: I have given solution in step2

Q: If we use the method of variation of parameters, the particular solution of the following…

A: We have to assume the appropriate solution first.

Q: 5. Solve the differential equation with method of undetermined coefficients. y" + 2y' – 3y = x + cos…

A:

Q: 1. What can you say about a solution of the equation y' = 49y² just by looking at the differential…

A: Given that : y' = 49y2. This is a differential equation and we find solution of this differential…

Q: 5. Find the solution of the differential equation using Variation of Parameters. у" - Зу" + Зу 3 E

A: Given y'''-3y''+3y'=exx

Q: y' + 2y = 2+ 3x

A:

Q: y" – 4y' + 4y = 2x

A:

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

A:

Q: y' = (4x + y)²

A:

Q: y(4) – 16y" = e¯* + sin3x y

A: find complementary function and particular integral and add them

Q: 4.Solve the linear differential equation for general solution y′′ + 16y = 0,

A:

Q: Find every nonzero solution of the differential equation y = y +2y°.

A:

Q: 5) Verify that y = 2e3 – 2x – 2 is a solution to the differential equation y' – 3y = 6x + 4. - -

A: Given that y=2e3x-2x-2    ......(1) Differentiating (1) with respect to x: y'=6e3x-2…

Q: Q5/: Find the general solution of non-homogenous differential equation using Variation of Parameters…

A: See this solution in below.

Q: If we use the method of variation of parameters, the particular solution of the following…

A:

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

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 18. The solution of the differential equation 2xy = x² + 3y² when y(1) = 3 is dx

A:

Q: Q5/: Find the general solution of non-homogenous differential equation using Variation of Parameters…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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: 12. Solve the second-Order differential equation: a²y dx2 -y = e* (use method of variation of…

A:

Q: (9))(y– 2x)y' = y %3D

A:

Q: 3. Find the particular solution to the differential equation (y + 5)(x+2) if the %3D dx solution…

A:

Q: 8- The solution of differential equation y" + 4y = 0 is.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If we use the method of variation of parameters, the particular solution of the following…

A:

Q: 3) Find the solution of the differential equation y = -ry + (/')².

A: The given differential equation is. y=-xy'+y'2                                .........1 This can be…

Q: What is the General and Particular solution of the Differential Equation 2x(y+1)dx-ydy=0? Where x=0…

A:

Q: 5. Find the solution of the differential equation using Variation of Parameters. y"' – 3y" + 3y' =

A: We will use the method of variation of parameters to solve this question. First, we find the three…

Q: y" + y' – 2y = 0

A:

Q: 4. The Bernoulli's form of the differential equation x²dy + (2xy-y³)dx=0 is

A: