dy = 4sin( 2x) and y=2 when *x= dx Suppose What is the particular solution to the given differential equation? 2

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: -(* +2) Solve for y = y (a) in the differential equation dy if y (0) = 1. No need to isolate y. %3D…

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Q: (x3 + ) dx + (y² + In x) dy = 0, is exact differential equation.

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Q: For which values of n is the function ya solution of the differential equation xy"-Kxy'-6y=0

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Q: dy + ( 1+x)y = e -× sin2x dx

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Q: III. dy y³ dx x²y-xyz

A: Sol:- y' =y3x2y-xy2Substitute y=vx, v is a function of xxv' +v=v21-vRewrite in the form of a first…

Q: The indicated function y1(x) is a solution of the given differential equation. Use reduction of…

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Q: Assume that the rate of change in y is proportional to y. Solve the resulting differential equation…

A: Given  dydx=ky Points on the curve 3, 3 and 4, 6

Q: I. dy tan(x) dx Cos (x) + x²

A: Given equation is dydx=tanxcosx+x2   What is the best way to solve the First Order Differential…

Q: xy"+y'=0; y1=ln(x) How can this second-order differential equation be solved by general solution?

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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: When à = 0 the differential equation becomes X" = 0 which gives the solution X = ax + b.

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Q: II. dy dx 2x² x(y² + 1)

A: We have to find the best way to solve the given First Order Differential Equation by Finding…

Q: How can you sometimes solve a differential equation of the form dy/dx = ƒ(x)?

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Q: Show complete and detailed solution Solve the differential equation: xy(dx-dy)=x2dy+y2dx if x=2,…

A: The given differential equation is; xy(dx-dy)=x2 dy+y2 dx if x=2, y=0.

Q: x3 Show that y = is the solution for the differential equation dx dy = 2x2 -

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Q: The differential equation dy/dx = y(y+6) has initial condition of y(0) = 3 What is y(1)? Multiple…

A: Given

Q: Find the particular solution to the differential equation when y(0)=3 and (2)=1

A: Given differential equation isy''=y'2x-y'x2-1 The conditions are y(0)=3,  y'(2)=1

Q: 3. (D² + 4)y = 10 cos 3x. ANS. Y = -2 cos 3

A: We have to find solutions

Q: Solve the differential equation for y if (1+9x²) dx %3D

A: Here we have to solve the differential equations,  1+9x2dydx=1.................................(1)

Q: Find the general solution of the differential equation: y' – 3y = xy. Use lower case c for the…

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Q: Find the particular solution to the differential equation y - y - 2y =- 2e when y(0) = – and y (0) =…

A: The characteristic equation of the given differential equation is m2-m-2=0. So,…

Q: What is the general solution of the differential equation; y’ = 2x cos (x^2)

A: solution:-y'=2x cosx2solving the differential equation we getdydx=2x cosx2y=∫2x cosx2 dxlet x2=t2x…

Q: If the differential equation is = ye", where x = 0, y = e. Determine the value of y when x = 1.…

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Q: Use separation of variables to find the general solution of the differential equation. dy 5x2 + 7 dx

A: Given:

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

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

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Q: Use the method of your choice to find the general solution of the following differential equation.

A: y'(t)=yt ∫xndx=xn+1n+1+C

Q: Find the general or Special Solution to the differential equation 2 y = (x-y₁²

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Q: Solve the differential equation dy/dx = ex-y + ex + e-y + 1

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Q: find the solution of the differential equation     dy / dx = y / (y-x)  with y(5) = 2

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

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Q: Solve the differential equation y Pemer 6a y5 subject to the condition that y 3 when = 3.

A: Here we have to solve the given differential equation

Q: 5) Solve the differential equation given as dy (dz) ² dy +2- y dr² dr

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

A: This is Separable differential equation

Q: Solve for the General Solution of the given Differential Equation dx – (1+ 2xtany)dy

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Q: ) xy dx - (xt2) dy =0

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Q: Show that y = ce* + (x + 2)e²x is a general solution for the differential equation y' - y = (x +…

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Q: 2)By using y' = p substitution, solve the differential equation xy" = y' + x(y')².

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Q: Solve the differential equation 2 dy dy 1+ dx dx2 assuming x > 0 and > 0. dy dx

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Q: 4ху Find the solution to the differential equation dx which passes through the point (0, e). (In…

A: We first separate the variables:dydx=4xylny10lny10dyy=4xdxThen we integrate both…

Q: 20.Find the particular solution of the differential equation x +1) = x3 – 2y, given x = 1 dx when y…

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

Q: dy 5. Solve the differential equation = 7xy3 if y = 0.5 when x = 2. dx

A: Given query is to find the solution of the differential equation.

Q: 3x√y. For y is not

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Q: Use separation of variables to find the general solution of the differential equation. e*(y' + + 3)…

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Q: xydx + 2(x2 +2y)dy=D0; when x= 0, y= 1

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Q: 2 sin x Show that y is the solution of the differential equation xy'+y=2 cos x.

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Q: Solve the given differential equation by separation of variables. 2 y In(x) dx = (y + ¹)² X

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