1. Solve the initial value problem dx - x* (1+ y) = 0, y(0) = 5.

Q: Solve the initial value problem: dy = x(1+ y)²; dx y(0) = -3

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Q: , solve the initial value problem.

A: dydx=yln y1+x2

Q: Solve the initial-value problem (4y−cos y) dy /dx −3x2 = 0, y(0) = 0

A: 4y-cosydydx-3x2=0 On simplification, we get ⇒4y-cosydydx=3x2⇒4y-cosy dy=3x2 dx Now integrating on…

Q: 3. Solve the initial-value problem: 2 dy = 2xy + 3y y(1) = dx 1

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Q: Solve the initial value problem (7). dX 2, X() = (). -3 1 X + -2 1 dt

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Q: 5. Find the solution of the differential equation y =- xy + xy³ (Bernoulli)

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Q: Find the explicit solution of the initial value problem, X +y = x² ln(x) y² where y(1) = 2 and x >…

A: The equation of the form dydx+P(x)y=Q(x)yn is Bernoulli's equation. The equation is converted into…

Q: Solve the initial value problem dy/dx=2/x+1, y(0)=2.

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Q: Solve the differential equation dy/dx =x/y2 with initial condition y(0) = 2.

A: Given : dydx = xy2

Q: Solve the initial value problem. dy -=x°(y- 3), y(0) = 8 dx

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Q: Find an explicit solution of the given initial-value problem. dyy²-1 = y(7) = 7 dx x² y =

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Q: Find an explicit solution of the given initial-value problem. x2 dy=y-xy, y(-1) = -4 dx y =

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Q: Find an explicit solution of the given initial-value problem. x20Y = y - xy, y(-1) = -2 dx y =

A: Given initial value problem, x2dydx=y-xy,y-1=-2 Find the explicit solution of this problem.

Q: Solve the initial value problem. dy + 3y – e -* = 0, y(0) = dx 2

A:

Q: 4: A- Solve the differential equation subjected to the condition y0)=1 dx

A: Firstly separate the variables and integrate on both sides and solve the differential equation.…

Q: Solve the initial value problem dy + X, x > 0; y(2) = 0 x3 dx

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Q: The solution of the separable differential equation = (1+y²)x is: %3D dx

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Q: 6. Solve the initial value problem: dx (x² + 2y²). = xy, y(-1) = 1 dy %3|

A: First of all write the given initial value problem in MDX+Ndy=0 form which is the homogeneous…

Q: initial-value

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Q: Solve the initial value problems dy/dx = 10 - x, y(0) = -1

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Q: 6. Solve the initial value problem: (2² + 2y^) Jy dx = xy, y(-1) = 1

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Q: 1. Sketch the graph of the solution of the initial value problem. Hint: You are not asked to solve…

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Q: What is the particular solution to the differential equation y -2x 3y2 – 2 with y 1 when dy x= 1?

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Q: dy/dx= 2ex-e-x y(0)=5

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Q: Solve the initial value problem: (4y + 2x – 5)dx + (6y + 4x – 1)dy = 0, y(-1) = 3 Clearly label your…

A: Initial Value Problem: In multivariable calculus, an initial value problem is anordinary…

Q: B/ Find solution for the homogenous differential equation below: dy x² +y² dx 2хy

A: Given differential equation is dydx = x2+y22xy

Q: 2. Solve the differential equation dy + xy = xy "Bernoulli" dx with y(0) = 1/2.

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Q: Solve the initial value problem √y dx + (x - 2)dy = 0, y(3) = 9

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Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = -1/ 1-…

A: The given differential equation,1-y2dx-1-x2dy=0, y0=12

Q: Solve the initial value problem + y cos x = dx sin 2x, y(n) = 0)

A: To solve the given initial value problem.

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

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Q: The solution to the differential equation dx = -2y, with the initial condition y(0) = 2, is

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Q: Solve the initial-value problem dy/dx+(3/x)y=x^2+x, y(1)=4

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Q: solve the initial value problem. (x+1)dy/dx+ 2y = x, x >-1, y(0) = 1

A: Write the equation as linear differential equation.

Q: Solve the initial value problem (x² + 4)- dy + 3xy = x, y(0) = 1. dx

A: Given the differential equation,  (x2+4)dydx+ 3xy = x , y(0) = 1 (x2+4)dydx+ 3xy=x(x2+4)dydx=x -…

Q: Solve the initial value problems    dy/dx=(x2+1)/x2 , y(1) = -1

A: The given differential equation  is

Q: Solve the initial value problem dy/dx=x2−1, y(3)=7.

A: Given:

Q: Find an explicit solution of the given initial-value problem. 1 √1-y² dx √1-x² dy = 0, y(0) = = y =

A:

Q: Solve the initial value problems 1.dy/dx = 2x - 7, y(2) = 0    2. dy/dx = 10 - x, y(0) = -1

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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: 3. Solve the initial value problem of y(-1) = 0 dx x+3

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

Q: Solve the initial value problem. √y dx + (x-9)dy = 0, y(10) = 1

A: Sol:- ydx+x-9dy = 0 , y10=1It can be rewritten as :-ydx=-(x-9)dy

Q: 3. Solve the initial Value Problem x dy +(y-cos x)dx = 0, y )=0 %3D

A:

Q: The differential equation y'=xy² is subject to the initial condition y(2) = 1. Find the value of…

A: Given,         The differential equation y'=xy2 is subject to the initial condition y2=1.

Q: =e*", y(0)=1. dx Find the solution of the initial value problem

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Q: Solve the Initial value problem:   dy/dx= ((2y)/x) - 1 , y(1)=3

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Q: 3. Find the solution of the initial-value problem d'y_3dy +2y=e* dx y(0)=1, y'(0) = 0 dx Using…

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Q: 2. The particular solution of the differential equation x*dy + y*dx = xy(xdy – ydx) when x = 1; y =…

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Q: Solve the initial value problem dy/dx=(x+y+1)2-(x+y-1)2  where y(0)=1/2

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.