5. Solve the unknown function 2 = ay (1 – by) dx 6. Given y(0) = ½, solve = 3x?y2. 7. Derive the orthogonal trajectories of the family of hyperbolas ry = c.

Q: . solve for y(3) at h =1.5, given y(0)=5 using heun’s equation and euler’s method dy dx = 3e −x −…

A: Heun's method: Heun's method also known as Euler's modified method. It works in following steps. 1.…

Q: 4. Solve the initial value problem. dy a. = 3e* →, y = 6, when x = 0. dx %3D %3D

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Q: Use Euler's method with h = 1/4 to compute approximate values of y(1) for t.y'= y(sint), y(0)=2.

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Q: (Think Bernoulli) Solve implicitly dy dx - y = e²xy³

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Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xcos2y dx + tany dy = 0

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Q: Show if the the initial value problem is dy separable or not -=y²(1+x²) • dx vith the initial value…

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Q: 1. Find a particular solution in the given equation which satisfies the indicated conditions.…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Solve the initial – value problem: xtan sec2. dy C :y(3) =0 2. eesc?ydx-Vr sinydy =0 :y (In's)= 3.

A: we can solve these question by variable separation and homogeneous function technique of solving…

Q: 3. Determine the Particular solution of this equation In terms ofY (xy2)dx + e*dy 0, as x → 0, y ==

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Q: dy - y = xy2 dx

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Q: OBTAIN A FAMILY SOLUTION FOR GIVEN EQUATION: dy/dx=(9x+4y+1)^2 Solve on paper

A: Solution: Consider the given Differential Equation is dydx = 9x+4y+12       ...(1) Let u = 9x + 4y…

Q: In the study of a cable suspended between two fixed points (see (c) Suspended Cable. Figure 4.36 on…

A:

Q: Solve the initial value problem given below. dy – 16xy and y = -2 when x = -4 %3D | dx

A: Given: dydx=-16xy, and y=-2 when x=-4 i.e. y-4=-2. To Solve: The given initial value problem.

Q: Solve the following initial value problem: 1 dy + 2ry? + (2a²y – cos(y)). 0, y(1) = . dx

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Q: Solve the Bernoulli equation dy *+y = xy

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Q: 4. Solve the following equation by backward Euler's method and also trapezoidal method: 1 1+t² y'…

A: Introduction: There are many iteration tools that are used to solve an initial value problem…

Q: Show that if you differentiate both sides of xy +4x + 2y = 1, the re- sult is (x + 2) + y +4 = 0.…

A: we have to show that the differentiation of xy+4x+2y=1 will result in (x+2)dydx+y+4=0 and then we…

Q: 1. Solve for y, using the method of successive approximation. dy dx = x + y; y(1) = 1

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Q: 8) Find the general and particular solution for the following separable equation dy -.5y, y(0) = 2…

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Q: 3. Solve the problem y(t) – y(t) = 4t with initial condition y(0) behavior of the solution as t → o…

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Q: . Find a particular solution to the inhomogeneous equation y" – 9y/ + 8y = e* in the form y(r) = c-…

A: To find A particular solution to the inhomogeneous equation in the form y(x) =Ce^(2x)

Q: Find the solution of the initial value problem in explicit form: dy 7+ 12x x > 0, y(1) = 4 dx xy?

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Q: dy +y=(x-1)y' dx

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Q: Q2/Solve the following equation from t=0 to 1 with step size is 0.5 using Euler's Method. dy dx = y…

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Q: Solve the following initial value problem. = 0, y'(0) = 4, y(0) = 1 dx?

A: Consider the Initial value problem d2ydx2=0                          y'(0)=4,y(0)=1

Q: 6. Given y(0) = ½ , solve = 3x²y². dx 7. Derive the orthogonal trajectories of the family of…

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Q: (1+ In xy) dx + (-)dy = 0

A: See the attachment

Q: solve the initial value problem  x dy - (y + sqrt(y)) dx = 0, y(1) = 1

A: We know :

Q: Solve the following Initial Value Problem. dy/dt=sec^2(t)-sin(t), y(pi/4)=1 y=??????????????????

A: Given that: dydt=sec2t-sint, yπ4=1

Q: ædy – y(1+ In y – In æ)dx = 0

A: The given differential equation  is changed to  the variable separable form by using the…

Q: dx-(it 2x tany) dy-0

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Q: Solve the initial value problem given below. dy - 3y (-2 – y) dx

A: To Determine: solve the initial value problem.

Q: Solve the following equation to obtain the family of solutions.Show your solution. (9+y²)dx +…

A: Finding the solution of differential equation

Q: 4. Show that 3x²e"dx + (x*e" – 1)dy = 0 is an exact equation and then find the solution.

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Q: dy 2y = 2x/y %3D dx

A: The solution of the problem is given in the next steps.

Q: Solve the following Bemoulli's equation. 1. 5. 6y2 dx – x(2x3 + y)dy = 0 -

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Q: -olve the initial-value problem. (2.xy² +3x* )dx +(2xr'y+4y')dy =0, y(-2) =1

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Q: dy %3D 3 e*y* dx +

A: Givendydx+y3=exy4To Find:Solution of a given Bernoulli's equation

Q: The solution of dy=(6+2y)dx subject to the initial condition y=0 when x=0 is

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Q: Determine whether the equation (ye™y . 1 - =)dx + (xe®Y + y2 is exact. If so, solve the initial…

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Q: (1+ In xy) dx + (-)dy = 0

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Q: Find the particular solution of (2x²y² + xy' )dx + 3 y? dy 0 that satisfies the condition y=1 when…

A: To solve the following differential equation

Q: 8) Find the general and particular solution for the following separable equation dy = -.5y, y(0) = 2…

A: The solution as follows :-

Q: Solve the equation (4y+2x– 5)dx + (6y +4x– 1)dy = 0 subject to the initial condition y(-1)= 2.

A: Consider a first order linear homogenous differential equation of the form, Pdx+Qdy=0→1 where P=fx,y…

Q: Find the solution of dx - (1+2x tany) dy = 0

A: Given: dx-1+2xtanydy=0

Q: dx dy dx dy Use elimination to solve: + = e'; -= *+

A: