Express the solutions of the initial value problems in terms of integrals. dy dx = √(1 + x2), y(1) = -2

Q: Apply Duhamel’s principle to write an integral formula for the solution of  initial value problem…

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Q: Find the explicit particular solution to the initial value problem. dy 2= (x – 2)2; y(2) = 1 dx

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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. x dy - (y + √y) dx = 0, y(1) = 1

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

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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 (7). dX 2, X() = (). -3 1 X + -2 1 dt

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

Q: Find the particular solution for initial value problem.

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

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Q: 2. Solve the following initial-value problem. dy (x + 1)+ y = In x ; y(1) = 10 dx

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Q: Find an explicit solution of the given initial-value problem. dx 8(x2 + 1), dt IT 1 %3D 4

A: We need to find explicit solution.

Q: Find the explicit particular solution of the initial value problem given. dy/dx = ye^9x, y(0) = 10e

A: Given. dy/dx = ye9x  => 1/ydy = e9xdx

Q: Solve the initial value problem. dy =7- dx 1 y(1) = 11

A: Let's find.

Q: Solve the initial value problem. 6. dy dx (8 + x) 2 Y(0) = 8

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

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Q: Solve the following initial value problem. dy 1 --X, x> 0; y(6) = 3 dx x2

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Q: Solve the initial value problem. dy + 9xy = 4x, y(0) = - 3 dx

A: This question is related to differential equations, we will solve it using given information.

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

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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: Solve the given initial value problem by using the method of exactness.  xy dx+(2x2+3y2-20)dy=0,…

A: First identify M and N and check that the differential equation is exact.

Q: Solve the following Initial Value Problem. (exy+1)dx+(ex-1)dy=0    ,     y(1)=1

A: Solve the following Initial Value Problem. (exy+1)dx+(ex-1)dy=0    ,     y(1)=1

Q: Please help. State P(x), Q(x), and integrating factor v(x).

A: Given,

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

A: The given differential equation is dydx=x+1x2.

Q: Solve the Initial Value Problem. (1 – 3t)– dy - у %3D 0, у(2) %3D —4 dt

A: The given differential equation is 1-3tdydt-y=0...(1) The initial condition is y2=-4.

Q: Solve the initial value problem. 5x dy = 0, y(2)= 1 4xy + 4xy dx

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

A: Use substitution y^4=v and find integrating factor

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

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Q: Solve the initial value problem: dy/dx= (1/(2sqrt(x)))+2 y(1)=3

A: Solving the initial value problem.

Q: Solve the initial-value problems dy = Vx У(1) %3D2 dx

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Q: Solve the initinal - value problem dy dx » y(6)=0 COsx - Sinz +y 0Lx s0.5 Using (a) Com pute the…

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Q: Solve the initial value problem dy - y = 2e' + 8e5t dt with y(0) 10.

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Q: Express the solution of the initial value problem y" + 9y = g(t), y(O) = 2, v'(0) = 1 in terms of a…

A: The solution is given below

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 initial value problem: dy/dx= (5x^4)(y^4) ; y(0)= 1/2

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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 given separable initial value problems 1)dy/dx=-2     y=3 when x=0

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Q: Find the solution of the initial value problem ty' +2y-2 sint, y(x/2)=1,

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Q: Solve the initial value problem. dy + 5xy = 8x, y(0) = - 6 dx y =

A: topic - differential equations

Q: Solve the initial value problem. dy 2xy = 8x, у(0) — 0 dx y =

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Q: Solve the initial-value problem dy + dx 2 e* + 1 \x – 1/ (х — 1)2 y(0) = 2

A: Given: dydx+2x−1y=ex+1(x−1)2

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

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Q: Find an explicit solution of the given initial-value problem. dy y (2) = 2 %3D dx x2-1

A: An equation which involves the derivative or differential coefficient is called differential…

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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Q: Solve the initial-value problem. dy (x² + 1) Y + 3x(y – 1) = 0, y(0) = 7 %3D dx

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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.