If y = f(x) is the solution of y' – 3y =-12.e 9z, f(0) =1, then

Q: Find the exact solution y to the initial-value problem dy/dx= x y^(1/2), y(1) = 4.

A: It is exact solution to the initial value problem.

Q: The differential equationy2y - v3 Y* -o after using substitution y=vx will convert into separable…

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

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

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

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Q: Find the particular solution of the differential equation (y + 1)dx – x dy = 0 if x=1 when y=0.

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Q: Find the solution to the initial-value problem. dy = y³xe*, y(0) = 1 dx II

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

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Q: Find the particular solution for initial value problem.

A: dydx=8x3-3x2+7x having initial value y3=0

Q: The function f (x) = e-® + 1 is a solution to the initial-value dy problem dx 1 -, y (0) = 1. True…

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Q: Find an explicit solution of the given initial-value problem. x2 dy = y − xy, y(-1) = -3 dx y =

A: We can solve as follows

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: initial-value

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Q: Obtain the particular solution satisfying the initial conditions indicated. 1. e* (3x°y-x)dx+e" dy =…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find an explicit solution to the initial value problem: dy = dx y(x) = ex - 5y y(0) = 0

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Q: The differential equation of the form M (x, y) dæ + N (x, y) dy = 0 that has been transformed to M1…

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Q: Find the solution of the given initial value problem- dy y = xe", y(1) = e - 1, x > 1 dx

A: The given initial value problem is  dydx-yx=xex, y1=e-1. Find the solution of the initial value…

Q: Solve the initial value problem: y(x) = 2x - 4y√x² + 1. dy dx = 0, y(0) = -4

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Q: Solve the given initial value problem for y=f(x) 1) dy/dx=3x-2 where y=2 when x=-1

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Q: Find the solution of the initial value problem dy 2 - - 4y + 0, y(1) = 2 dx

A: Given differential equation is −xdydx−4y+2x2=0......1 and y1=2. We have to find the solution of the…

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

A: f''(x)=3x2integrating both side∫f''(x) dx=∫3x2 dxf'(x)=3x33+cf'(x)=x3+c ---------equation 1Now…

Q: Find the particular solution of the differential equation determined by the initial conditions, d^2…

A: The solution is as shown below

Q: Find the particular solution of the differential equation. x dy/dx  + 5y = x2; y = 12 when x = 2

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Q: Use separation of variables to solve the initial value problem. dy 2xcos² y; y(3) = 0 dx

A: Here we have to solve the givne differential equation.  dydx=2xcos2y; y(3)=0

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

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Q: Find the general solution of the Bernoulli equation 2yy′= y^2+ t + 1.

A: To solve given differential equation first we solve for rearrange the equation in the form of first…

Q: Find the function that solves the initial value problem dy 10x + 3, y(1) = 0. dx y(x)

A: According to question,Given differential equation,dydx = -10x+3,y1 = 0

Q: Find an explicit solution of the given initial-value problem. x2 dy = y - %3D у — ху, у(-1) %3D -1…

A: Firstly we will solve the given differential equation by using variable separable form then…

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: Find an explicit solution to the initial value problem dy/dx = 2xy +3y, y(0) = -2

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Q: The differential equation 3y(x² –1)dx+(x² +8y– 3x}dy = 0; is exact because ƏM ƏN dy Əx

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Q: Find the solution of the initial value problem. dy y - 2, y(0)=3 dt 1+t

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

A: Given information: Concept Used:

Q: Find an explicit solution of the given initial-value problem. V1- y? dx - V1- x2 dy = 0, y(0) = . y…

A: Solve the following

Q: Find the solution of the initial value problem subject to the indicated initial condition in terms…

A: solution :-

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

A: Consider the given function as f'x=9x2+1, f0=7

Q: 2. Find the particular solution of Vx2 + y2 )dx – x dy = 0 ; y = 1 when x V3. -

A: Given differential equations homogeneous differential equation of first order we will do the…

Q: Use separation of variables to solve the initial-value problem. dy 7. 25 - y? where y < 0 and y(0) =…

A: Given below answer with detailed steps

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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

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Q: function y(t) is a solution of the initial value problem y" + ay' + by = 0,

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Q: (2xy +y) dx + (x²- x ) dy = 0

A: Given: (2xy+y)dx+(x2-x)dy=0, y(0)=e

Q: Find the solution of the initial value problem dy = -y+e'y?, y(-1) = -1 dt

A: We have to find the solution of the initial value problem…

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

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Q: Find the particular solution to the differential equation y′′+4y′=0 that satisfies y(0)=1 and…

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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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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.