Solve the initial-value problems. dy _ 1 dy x+1 a.- dx dy - = x²/x³; y(0) = 0 2- y(-1) = 5 ; y(1) = 0 dx 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: Solve the separable differential equation dy 7x – 6yVx² +1 = 0. - dx Subject to the initial…

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Q: 3) Find the solution of Initial Value Problem dy 2x-sin y dx 2x cos y ; y(4)=0

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

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Q: Solve using separable differential equations dy 1 dx y3

A: We have to solve using separating the variables. xdydx=1y3

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

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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. dy 3 dx - = x˚ (y - 5), y(0) = 9

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Q: Solve the differential equation dy 1 dx Зу3 By the method of separating the variables

A: To solve the given differential equation.

Q: The particular solution of the differential equation x^2 dx - (y+1) dy = 0 if y(0)=1 is -:

A: The given differential equation is x2dx-(y+1)dy=0, y(0)=1. Solve the given differential equation to…

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

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Q: dy y- 1 dx -1' y(2) = 2

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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

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

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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: Solve the initial value problem. dy = 4 e -X, y(0) = 1, y'(0) = 0 2 dx

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Q: Solve the initial value problem (dx/dt)+2x=cos(4t) with x(0)=−2. x(t)=?

A: Solve the initial value problem

Q: Obtain the General Solution (x-1 )dx - (3 x -2y -S) dy = 0 MAM

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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: The differential equation dy/dx = y(y+6) has initial condition of y(0) = 3 What is y(1)? Multiple…

A: Given

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: Solve the initial value problem dy/dx=2x−1x2, x≠0, y(1)=5.

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Q: 1 dy Solve the initial value problem of - 2 dx y +1 cos x , y(n) = 0

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Q: 6. Verify that y(x) = /E+ 9 is a solution of the initial-value dy problem 1 and y(0) = 3. 2y dx ||

A: To verifyy(x)=x+9 is  a solution of the given IVP dydx=12y

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

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Q: (b) Find an explicit solution to the initial value problem given by (y – 1) dx + x² dy = 0, y(1) = 0…

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Q: Solve the differential equation (y+xy+ 1) dx + (x²+xy²+2y) dy=0 by forming integrable combinations.

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

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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: Use a technique of integration or a substitution to find an explicit solution of the given…

A: To find the solution of the differential equation we use the method of separation of variables. We…

Q: Find the solution of the given initial value problem in explicit form. π ㅠ sin (2x) dx + cos(7y) dy…

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Q: Find an explicit solution of the given initial-value problem. √2 √₁-y² dx - 1- √1-x² dy = 0, y(0) =…

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

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Q: Find the solution of the given initial value problem in explicit form. sin (2x) dx + cos(7y) dy = 0,…

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

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

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Q: The general solution of the differential equation xy'dx + exp(x:) dy is:

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Q: Solve the differential equation 2 dy dy 1+ dx dx2 assuming x > 0 and > 0. dy dx

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

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Q: Find an explicit solution of the given initial-value problem. √1-y² dx - √1-x² dy = 0, y(0) = 113 2…

A: Here in this question, we have to find out the solution to the given differential equation.

Q: 1. Solve the initial value problem. dy -= f'(x) = x* - x³ +x – 1, f(0) = -3 dx

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Q: Solve the differential equation (y+xy+1)dr +(x²+xy²+ 2y)dy=0 by forming integrable combinations.

A: Differential equation

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

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Q: Use a technique of integration or a substitution to find an explicit solution of the given…

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Q: Solve the differential equation: dy 1 1 1)y – x +1 = 0, y1= ax - - dx

A: The given differential equation is dydx-y2x-21x-1y-x+1=0. Substitute y=ax in the above equation and…