dy x²e&"; _y(0) = ´dx

Q: Find the particular solution for initial value problem.

A: x2dydx-yx=0⇒x2dydx=yx⇒dyy=xx2 dx⇒dyy=x12·x-2 dx⇒dyy=x-32 dx Now integrating on both sides, we get…

Q: Find the general solution of each differential equation, and when initial conditions are given, the…

A:

Q: , solve the initial value problem.

A: dydx=yln y1+x2

Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. y' = y2 y =…

A:

Q: determine if the equation below is seperable. If it is, solve the given initial value problem

A: Check whether the differential equation is separable or not

Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A:

Q: Solve the initial value problem dy – y = 6e' + 72et dt with y(0) = 4.

A:

Q: Solve the initial value problem dy/dx=x^2+1/x^2, y=-1 when x=1.

A:

Q: Solve the initial value problem. dy 3 dx - = x˚ (y - 5), y(0) = 9

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Q: Find the particular solution for initial value problem.

A:

Q: Find the general solution of each differential equation, and when initial conditions are given, the…

A: 11. y'-2y=y2, y(0)=3Put…

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.

A:

Q: plve the initial value problem given by y" + y = (x – 1)*, y(0) = 0, y'(0) = 0

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Q: Problem 2.3 i. and 2.3 ii

A: Given initial problems are

Q: Solve the initial value problem given by ty" – ty – y = e', y(0) = -1, y'(0) = 0

A: Given the initial value problem            ty''-ty'-y=et, y(0)=-1, y'(0)=0 Solve it.

Q: ) Write the solution of each initial value problems as integral equation, integrate if possible and…

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Q: Solve the initial value problems d2y/dx2 = sec2 x, y(0) = 0 and y'(0) = 1

A: The given differential equation is: y(0)=0 y’(0)=1

Q: Solve the initial value problem: dy d x COSI

A:

Q: What integral equation is equivalent to the initial value problem y′ = ƒ(x), y(x0) = y0?

A: Write y'= dy/dxThen separate the variables.

Q: initial-value

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Q: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. y' = y2 y =…

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Q: Solve the initial value problem. dx dt -4tx=t Int+3, x(1) = 0

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Q: Solve the initial value problem y′+ysinx=sinx and y(π/2)=1

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Q: Q/ Findl the Partial differential equation by climinating the arbitrar function %D

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

A: Explanation: Given that,  dydx-x6(1+y)=0, y(0) Now,  dydx=x6(1+y)1(1+y)dy=x6dx

Q: Find the function which solves the initial value problem dy/dx=2x−2, y(2)=−7 y(x)=?

A: The solution is:

Q: Solve the initial-value problem. dy/dx= x4/5, for x greater than or equal to 0 with y(0)=3

A: Given,

Q: Solve the initial value problem. dy 8x, y(0) = 6 = dx

A: The differential equation is given by dydx = 8x3, y(0) = 6 To evaluate : The solution of the…

Q: Verify that the function y = Ce5x is a solution of the differential equation           y′ = 5y

A: The given function is  y = Ce5x  The differential equation is y′ = 5y

Q: 2 Solvehe initial value problems below. dy dt

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Solve the initial value problems dy/dt = et sin (et - 2) , y (ln 2) = 0

A: Given: dydt=etsinet-2

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

A:

Q: 9. Find the particular solution for each initial value problem. a) (2x + 3)y = where y(0) = 1 dx b)…

A: Particular solution:         The solution obtained by giving particular values to independent…

Q: Solve the initial value problem dy/dx= 1+x+x^2/2, with y=1 when x=0.

A:

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: show that each function y = ƒ(x) is a solution of theaccompanying differential equation. 2y' + 3y =…

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Q: dx 10x – x2, dt x(0) = 1 -

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Q: Solve the initial-value problem. xy' = y + 2x² sin(x), y(¹) = 0

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Q: Solve the initial value problem y"+y = cosx; y(0) =1,y'(0)=-1

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Q: Solve the initial value problem (dy/dt)−y=3et+45e6t with y(0)=5.

A: Consider the given differential equation with initial condition.

Q: Solve the initial- value problem:

A: We are given the Problem: ⇒dydx=cos x-sin x+y ⇒dy=(cos x-sin x+y)dx Now , integrating both sides, we…

Q: Find the particular solution for each initial value problem.

A: The given differential equation is, dydx+3x2=2x We need to find a particular solution when the…

Q: Find the particular solution for each initial value problem.

A: Given:  2x+3y=dydx; y(0)=1 To Find: Solution of given equation

Q: Find the function which solves the initial value problem dy/dx= 3ex −2x;  y(0)=−1.

A: Given that dy/dx = 3ex-2x;   y(0) = 1.dy = (3ex-2x)dx            (By cross multiplying)Integrate on…

Q: Solve the following initial value problem: y' (In x) with y(1)=0. xe

A: Use method of separation of variable and integrate with given initial value.

Q: Find the particular solution for each initial value problem.

A:

Q: Find the particular solution of the differential equation that satisfies the initial condition(s). f…

A:

Q: solve the inhomogeneous initial value problem x = (; ) × (4 ln t X + 1 -2 X(1) = (1). %3D

A: Given,              X˙=2-41-2X+ 4lnt1t,     X(1) = 1-1                        (1)

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.