dy ey-x sec y (1 + x²) У (0) 3 0 dx ||

Q: The solution of dy/dx = y with initial value y (0) = 1 bounded in the interval (a) - 0 1

A: Bounded solution in the interval

Q: Solve the initial value problem e*dx + (e*tany + 2secy)dy = 0, y(1) = 2

A: Given that exdx+extaby+2sec ydy=0, y(1)=2. This is of the form Mdx+Ndy=0. M=exMy=0 And…

Q: 1. Test for exactness and find the particular solution of dx + + dy = 0 (1 – xy)? (1 – xy)² |

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution is: ∫Mdx⏟Take…

Q: b) Use the initial condition y(0)= 2.14 to find the particular solution of dy -2y + x2 + 2x = 0 dx…

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Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

A: Gg

Q: dy =, with initial condition y(0) =2 is dx y The solution of %3D

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Q: Show that y2 +x – 3 = 0 is an implicit solution to dx dy on 2y the interval -o to 3

A: To show that  y2+x-3=0...(1) is an implicit solution to dydx=-12y on the interval (-∞,3)

Q: Solve the initial-value problem. dy for x21 with y(4) = 4 %3D dx The solution to the initial-value…

A: We have to solve the initial-value problem: dydx=5x Solving by variable separable method,…

Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: ) Obtain the particular solution of (2x-3y+4)dx+3(x–1)dy =0; when x =-1, y = 2 O Find the general…

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Q: Solve for the given DE: y(y^3-x)dx+x(y^3+x)dy=0

A: first we will check this is exact or not this is not exact then we will find its integrating factor…

Q: [  (1+ xsiny)dx - x2cosydy = 0  ] How can I find the solution "y" of this equation?

A: We shall use basic knowledge of first order ordinary differential equations to solve this question.…

Q: 1- xy dy + (x² + y² )dy = 0 dx 2- 2. dy – y = ex/2 3- (x + 2y)dx – xdy = 0 dy 4- cosh x+ (sinh x)y =…

A: As per the guidelines we can solve 2 problems.

Q: Apply classical fourth-order Runge-Kutta method to solve dy dx f(x,y) == 4e®** –0.3y , using h=0.5…

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Q: Find dy/dx by implic differatiation. a) x^3-xy^2+y^3=1

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: Solve the initial value problem for y as a function of x. x2 - 16 dy = X, x > 4, y(8) = 0 dx

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Q: Solve the differential equatons (2x + Y I+ x²yª 1. dx 1+ (xy)2/ dy

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Q: To be able to solve the differential equation dx = sin(x - y), use the substitutions A z = x- y, dz…

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Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx – (3x- y – 4)dy = 0

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Q: a. Find the General and Particular solution of dy/dx = −8 sin 4x ; y = 6 when x = 0

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

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Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: Solve the D.E [Y(1+1/x)+cosy]dx+[x+lnx-xsiny]dy=0

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Q: Use the Runge-Kutta method to solve 10(dy/dx) = x2 + y2, y(0) = 1, for the interval of 0<=x<=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: Solve the equation dy/dx=1-y , given y(0)=0 using modified Euler’s method and find y at x=0.1 and…

A: Given differential equation is, dydx=1-y, y(0)=0. To find the solve the differential equation using…

Q: obtain the general solution. xcos^2 ydx +tanydy =0.

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

Q: the solution to the IVP(x2+y2)dy/dx+xy=0 with y(0)=2 is

A: Given DE is x2+y2dydx+xy=0  and y(0)=2 find the solution of the DE

Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

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Q: dy dx ycos X こ y(o)=1 I +2y2

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Q: Find the general solution of (x +1)3d²y dx? 1TE + 3(x + 1)² + (x+ 1)y = 6 ln(x +1). dy dx

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Q: dy-5+4y =16x+20e" dx ; y(0) = 0, y'(0) =1 dx

A: Given differential equation d2ydx2-5dydx+4y=16x+20ex. The Auxiliary equation is…

Q: Solve the general Solution of:  (xsiny/x- ycosy/xdx)dx + xcosy/x dy=0

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Q: Find all initial conditions such that (x^2-x)y'=(2x-1)y has no solution, precisely one solution, and…

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Q: Find the particular solution of the equation 2(x +3) dy – xy dx = 0 %3D - tisfying the initial…

A: Given: 2(x+3)dy-xydx=0     satisfying the intial condition x=-2 and y=1

Q: Use separation of variables to solve the initial-value problem. Give an explicit solution to the…

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Q: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

A: Given: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

Q: 1. e (3xy-x)dx+e* dy = 0; when x = 0, y = -1 4 Ans. y =-- 1 3

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Q: dr2 dx dx d²y, 7 dy , 9y 3. dr2 dy =1 at x = 1. dx = 0; y = 0 and x dx x2 4. Use the method of…

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Q: Derive the general solution of dy 1. dx y

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Q: Find the general solution of the DE sec x dy = y dx. O In y = e^x +c O In y = sin x + c

A: Our Aim is to find the general solution of the differential equation given below:-sec (x) dy=y dx…

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

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Q: solve the simultaneois equation (dx)/(dt) = 3x + 2y (dy)/(dt) + 5x + 3y = 0

A: Given simultaneous equation, dxdt=3x+2ydydt+5x+3y=0 The eigen value of a matrix is calculated by…

Q: Test for the exactness and find the implicit solution to [2x+ ycos(xy)]dx + xcos(xy)dy= 0 when X =…

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Q: What is the appropriate substitution to solve dy/dx + ln(x+1)y/x = x^3y^3? z=y^-2 z=y^2 z=y^3 y=vx

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find the particular solution of (2x²y² + xy' )dx + 3 y? dy 0 that satisfies the condition y=1 when…

A: To solve the following differential equation

Q: Solve the homogenous DE Solve: xy dx - (x + 2y)^2 dy = 0.

A: