3. Find the general solution of differential eguation y" - v' - 6y = 0

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: 4. The Bernoulli's form of the differential equation x'dy+ (2xy-y')dx=0 is

A: Given problem:- The Bernoulli's form of the differential equation x2 dy + (2xy - y3)dx = 0

Q: What is a particular solution to the differential equation 2y dx – 3x dy = 0 when x = 1 and y = 1?

A:

Q: 13 Find solution of non-homogeneous differential equation (D* +1)y = sin (3x)

A: Find complementary function and particular integral

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

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Q: 3. Find the general solution of this separable differential equation. dy y cos x dx sin x + 2

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Q: Show that y = sin−1 x satisfies the differential equation y = sec ywith initial condition y(0) = 0.

A: The given differential equation is y' =  sec y,  with initial conditions y(0) = 0.We want to show…

Q: Find the solution of the differential equation that satisfies the given inital condition.…

A:

Q: 2. Solve the first-order linear differential equatio a. y' + 3y = e3x

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Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

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Q: Find the particular solution of the differential equation with the initial condition given below.…

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Q: 9. For the differential equation condition y(0) = 1. dy -- y = ey², solve for y = f(x) given the…

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Q: The Bernoulli's form of the differential equation x³ydx + (3x¹ − y³ )dy = 0 is

A:

Q: 4. The degree of the differential equation (y")³ + y' – cos y = x is

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Q: 2x-y? xy? 3- ()dr – ()dy = 0 is exact differential equation. True False o o

A:

Q: Suppose that x = 0 is a regular singular point of the differential equation 4xy" + 2y' + y = 0 Then,…

A: Given: x=0 is a regular singular point of differential equation 4xy''+2y'+y=0. To find: Indicial…

Q: 5. Find the general solution to the differential equation et y" – 2y' + y 1+ x2 (where y' = )

A: Let us consider the differential equation y''+py'+q=g(x) To solve the equation  Determine the…

Q: Determine the complete solution of the differential equation y" + 4y = 2cos2x %3D subject to…

A:

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: 3. Plot the slope field for the differential equation = y² – x and sketch the solution for the…

A: Given: A differential equation dydx=y2-x. To sketch: Slope field of given differential equation and…

Q: If 2x3+3ycos(xy)+(cx2y2+3xcos(xy))y'=0 is the exact differential equation then c =?

A: The exact differential equation is defined as the differential equation of the form Mx,ydx+Nx,ydy=0,…

Q: Obtain the general solution for the following differential equation using Separation of Variables…

A: Using method of seperation of variables

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

A: I have given solution in step2

Q: What is the particular solution to the differential equation dy/dx=xy2 with initial condition y(2) =…

A: To find the particular solution

Q: (D – 3D + 2) y = (1+ e-")?

A: I am attaching image so that you understand each and every step.

Q: y(4x + y) dx - 2(x² - y) dy = 0

A:

Q: 2. Find the solution of the differential equation that satisfies the given initial condition. dy…

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

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Q: 6. Find the general solution of the following differential equation using variation of parameters.…

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Q: what is the particular solution to the differential equation dy/dx=3sin(x)(2-y)with the initial…

A: You need to apply variable separable metod to solve the given differential equation.

Q: 1.) Obtain the general solution of the differential equation dx – (1 + 2x tany) dy = 0.

A:

Q: x²y" + xy' + (x² – 1)y = 0 about the point x = 0.

A: The objective is to find the series solution of differential equation x2y''+xy'+x2-1y=0 avout the…

Q: Find the general solution of the non-homogeneous differential equation Y” –  2Y’  + Y  =  4 cos x

A:

Q: 2) find the complete solution of the differential equation x dy +Jx²-y*dx = ydt

A: given xdy+x2-y2dx=ydxxdy=(y-x2-y2)dxdydx=(y-x2-y2x)put…

Q: 1. The order of the differential equation 5x- d'y aty + 3x + w'y = 0 is

A:

Q: Show that the solution curves of the differential equation y(2x3 – y3) dy x(2y3 – x³) dx are of the…

A: Given equation is Homogeneous differential equation of 1st order.

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: Solve the differential equation dy/dx=5-x/y with the inital condition y(6)=-4.

A: We have to solve

Q: 4. Given that x=0 when y = 8, show that the general solution of the differential dy equation (x +4)…

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Q: 3. Find the general solution of the differential equation y(4) - 4y" = t² + et.

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Q: Show that (y^2-1)^2=Ax is the general solution of the differential equation 4xy dy/dx =-1+y^2.

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Q: Obtain the solution of the differential equation (3 sin y − 5x)dx + 2x^2cot y dy = 0

A: Given the DE is 3siny-5xdx+2x2cotydy=0.

Q: Consider the differential equation y = x+ y. Use Euler's method with Ax = 0.1 to estimate y when x =…

A: Let fx,y=x+y. Substitute 0 for n, 0.1 for h, -1 for x0 and 0 for y0 in the Euler's formula…

Q: 3. Verify by direct substation that y = > Cn x", is a solution of this linear differential equation…

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Q: What is the particular solution of the differential equation (x+y) dx + (x - y) dy = 0 when x = 0…

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Q: Find the general solution of the given differential equations. y" – y' – 2y = cosh(2x)

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Q: 4. Find the general solution of the differential equation using the method of undetermined…

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Q: 4. Use separation of variables to find the general solution of the differential equation. dy = 5t*…

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Q: Consider the differential equation (10x³y* + e=y + 3 sin(4x + 3y))y' + (6x²y5 + 4 sin(4x + 3y) + 2)…

A: