1. Find the general solution of y (x² + y² ) dx + x (3x? – 5y² ) dy = 0

Q: obtain solution of this differential equation (1-xy)-2dx+[y2+x2(1-xy)-2]dy=0 when x=2 and y=1…

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Q: 1. Show that if you differentiate both sides of x2 + 2y³ = 6, the result is 2x + 6y2 = 0. Then solve…

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Q: Use Euler's method with step size 1 to estimate (¹), where y() is the solution of the problem y +…

A: Given that y'+3x2y=x2 Using Euler's method, find the value of  x at 1. Initial conditions are y0=3…

Q: 1- Solve = cos x + y, where y = dy dx 2.0 at x 0 take step size h = Ax= 0.1 and solve for 0 ≤ x ≤…

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Q: 3. Find for the simplified general solution of (1 + x³)dy - x²ydx = 0

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Q: 1. Linear equation of order one: dy-(r-2ydx =0

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Q: What can be the method of solving the DE? 2xyy' = y² – 2x³3 Bernoulli's DE Substitution suggested by…

A: Let's find which method is suitable.

Q: Solve dy/dx = y -x with y(0) =1 using the linear multi-step method Yi+1 +(3/2)yı -3yı-1 +(1/2)yi-2 =…

A: First solve the given differential equation: Given : y'=y-xy'-y=-x The given differential equation…

Q: A hand-held calculator will suffice for this problem, where an initial value problem and its exact…

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Q: Find the differential equations of the families of curves: Parabolas with vertex on the x-axis and…

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Q: The method of undetermined coefficients can sometimes be used tosolve first-order ordinary…

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Q: Write down all possible methods in which the (х- differential equation 2x = 2y) dx/dy can be solved.…

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Q: dy/(3x2) = (1 + y²)1.5 dx.

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Q: 1. Set up the initial value problem for finding the equation of the curve that passes through the…

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Q: The partial differential equation is to solve: XUx + YUy = 0, with U(0,Y)=e-y^2  and i have that the…

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Q: 2. Find the general solution of (2x-3y-2) dx-(x-2y)dy = 0

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Q: Find the differential equation of the family of circles with centers on the line x – 2y = 3 and…

A: Given:  circles with centers on the line x – 2y = 3and passing through (3, 0).

Q: Attached below is a description and the necessary differential equations systems problem. What is…

A: Questions from differential equations.

Q: ① Solveing dy - - x dx = 。 ㅎ

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Q: Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete…

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Q: 11.Solve dy - x+) y(2) = 2 by Fourth order Runge-Kutta Method at x = 2.5, and x = 3 %3D dx

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Q: Solve the initial value problem given by y' = (x − y)2 ,  y(0) = 0 What is the interval of…

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Q: The differential equation dudx=5u+10  admits one equilbrium solution that is    asymptotically…

A: The given solution is  unstable whose plot is shown below.

Q: 2. Consider the second-order nonlinear system differential equation * +*+ sinx = 0 Try to find…

A: We know that,

Q: What is the value of the coefficient d of the equation y = ax + bx² + cx + d so that it will have…

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Q: 3. (x² – xy + y²)dx – xy dy = 0

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Q: 3. The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Here we will use two formula  1st Area of triangle  If two sides of a triangle has length a and b…

Q: (3tanx-2cosy)sec²xdx

A: We will solve the differential equation.

Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

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Q: (1 point) Use Euler's method with step size 0.1 to estimate y(0.5), where y(x) is the solution of…

A: Here, fx,y=2x+y2h=0.1y0=1 so, x0=0, y0=1

Q: Solve the problem := (1+ 4x)/y over the interval from from x = 0 to x = 1 using a step size of 0.25…

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Q: 4. Find the Differential Equation and Orthogonal Equation of the family of parabolas with vertex and…

A: Let the vertex lies at (a,0) and focus at (b,0) So the general equation of parabola having axis as…

Q: 2. Find the particular solution of (3sin y- 5x) dx+2x cot ydy = 0 ;y(-1)=-

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Q: 9. . sinh 3x dp- 1+cos 3x 2x+9 10. S x² +6x-4

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Q: 4) One of the solution of the equation y"(x) + p(x)y' (x) + q(x)y(x) = 0 is given by yı (x) =…

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Q: Describe two ways to find the general solution of (dy/dx) + 3xy = x. Verify that each method gives…

A: Given: The differential equation is dydx+3xy=x We have to find the general solution by two ways.

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: How do I solve this non-exact DE (4x+3y-7) dx+ (4x + 3y+1) dy=0?

A: Consider the substitution, z = 4x + 3y

Q: Find the differential equation of family of parabolas with axis parallel to the x-axis and with…

A: The general equation of family of parabolas with axis parallel to the x-axis, with a vertex at a…

Q: Q. Solve the boundary value problem d²y dx² And the initial conditions are y(0) = 1.5 and y(2.5)=-3…

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Q: Apply Euler's method to approximate the solution of the initial value problem y' = 2 cos(2x) cos(y),…

A: We have to find the value of y(2) using Euler's method for approximation.

Q: A/ By using Linear equation solve the first order differential uation y' + sec(x)y= cos(x)

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Q: Obtain the solution of the following differential equations. 4. (3x + y − 2)dx − (3x + y + 4)dy = 0

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Q: If the family of curve has 4 arbitrary constants then the corresponding differential equation is c)…

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Q: 3. (sin'x + cosv)dx - tanxsin2ydy = 0

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