In each of the following, obtain the family of solutions. 1. (x-y) dx + (3x+y) dy = 0 when x=2, y=-1

Q: Solve the following initial value problem. dy/dx  =  y2 − 9y + 8,    y(0)  =  3

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: solve the following diffrential c) x²(y+1)dx+(x²-1)(y-1)dy=0

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Q: In each of the following, obtain the general solution. 1. (1-x)y' = y 2. xy'dx + e*dy = 0

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Q: Obtain the particular solutions of the following: (y-Vr² + y² \dx– xdy =0, y(0)=1 a.

A: Solution is given below:

Q: Solve the following initial value problem. dy 1 -х, х > 0;B у(4) %3 3 2 dx The solution is. (Type an…

A: Solve the following

Q: In the given question , find d2y /dx2 implicitly in terms of x and y :-   xy - 1 = 2x + y2

A: In the given question , find d2y /dx2 implicitly in terms of x and y :- xy - 1 = 2x + y2

Q: Solve the following initial value problem (3x-y-5)dx + (x+y+2)dy =0; y(2)= -2

A: Answer

Q: 3. Find the complete solution of 2xdy – y(x + 1)dx + 6y³dx = 0

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Q: Solve the non-homo. D.E. 1.y" + y = 3e2x

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Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex²

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Q: Obtain the general solution of the following equations:    2y(x2-y+x)dx-(x2-2y)dy=0

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Q: Find the solution of the following initial value problem. dy 4 x, y(0) = 9 dx y =

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Q: Solve the following initial value – problems (4xy+ 3x2)dx+(2y+2x²) = 0, y(0) = -2 %3D

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Q: Solve each of the DE's 1. (D² +4)y = 4cos² x

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Q: Give the general solution of xy²dy = (x³ + y³)dx in explicit form.

A: Given differential equation is  which is homogeneous differential equation.

Q: Find the solution of the following 3(1 + t ^ 2) * (dy)/(dt) = 2ty * (y ^ 3 - 1)

A: The solution to the given differential equation is explained below.

Q: B- Solve one of the following initial value problems for y as a function of x: 2. %3D x²+1 dx 1,…

A: To solve the given initial value problem as a function of x

Q: Find the general solution or particular solution of each of the foll 1. 2y(x+y+2)dx + (y²–x²– 4x –…

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Q: Solve the following initial value problem. dy = 2+ Vy - 2r, dr y(0) = 9 %3D

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Q: Find the solution of the initial-value problem dy + 3r*y = x², y(0) = 2. %3D dr

A: First order differential equation of the form ; are known as Leibni'z linear equation. The solution…

Q: Obtain the general solution of the following equations:   (x-4y-9)dx-(4x+y-2)dy=0

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Q: Which of the following graphs represents the solution of the initial value problem y" + 36 y =…

A: Use Laplace transforms for solving the given IVP as follows. y''+36y=sin5.5 t, y0=0,…

Q: Solve the following initial value problem. dy +x, x> 0; y(2) = 5 .3 dx

A: Given: dydx=1x3+x, x>0; y(2)=5

Q: Find the complete solution of the DE (D3+6D2+11D+6)y=ex +cosx.

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Q: Solve the following initial value problem I) (3x2+2xy2)dx+12x2ydy, y(2) = −3

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Q: Solve the initia value problem: dy 1 and y(1) = 1. dr

A: To solve the initial value problem dydx=x-1x    and    y1=1

Q: Proceed as in this example and find an explicit solution of the given initial-value problem. dy = y?…

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Q: 12. Find the general solution of x²dx + y(x – 1)dy = 0

A: This is a variable seperable DE.

Q: Solve the following initial-value problems. 2. (4xy+ 3x2)dx + (2y + 202) = 0, y(0) = -2 %3D

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Q: Solve the initial value problem.

A: Given differential equation is: dydx=3x+23 ; y0=1 We have solve the above equation. Then we get,…

Q: Find the general solution of the given Attached equation

A: Differential eq:9d2ydx2+6dydx+y=0The auxiliary eq is 9m2+6m+1=0

Q: Find the solution of the following initial value problem. dy = 3 x², y(0) = 9 dx y =

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Q: Solve the following initial value problem by the method of separation of variables. dy 2x+1 ,y(0) =…

A: To solve the given initial value problem.

Q: Find the particular solutions of the following equations: dy 4r +y given y-4, when x=1

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Q: The equation y3 = 3Bx is the general solution of 3y Oy Oy 3xy Ou' = 3y

A: We will form the differential equation using given solution

Q: Find the general solution of (2x – y) dy = 2y – x - da

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Q: Find the solution of the following initial value problem. dy 4 x³, y(0) = 9 dx %3|

A: Firstly separate the variables in the given differential equation and integrate. ∫xn dx =xn+1n+1+C

Q: In problems  determine by inspection at least two solutions of the   1. x dy/dx =2y,  y(0)=0

A: Given: xdydx=2y, y0=0 for solving given differential equation we will use variable separable method

Q: Give the general solution of: dw/dx + (4w)/x = x3

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Q: Which of the following graphs shows the solution of the initial value problem dy -x, y = 1 when x =…

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Q: he initial value problem dy/dx = xy, y(0) = 0 has no solution. Is this True or False

A: Given: dydx=xy, y0=0 Using variable separable dyy=dxx Integrating both sides, we get  logy=logx+logC…

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

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Q: 5- The general solution of the following equation dy d²x 10+ 25y= 0 is dx

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Q: Solve the initial value problem dy d x e**y sin cex -4), y(ın 4)= -) こ

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Q: 2. 3(3x² + y² kdx – 2.xydy = 0

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Q: Solve the following initial condition problem: d2y/dx2 + 9y = 2 cos(3x); y(0) = 0; y′(0) = 1 /3

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Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D. Answer:

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