Eliminate the arbitrary constant. 1) y = Bx + B² + 1 Answer: y = y'x + (y')²+1 -a DE of 1* order and 2nd degree

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Q: 1.Solve the partial differential equation -7 = 0, by method of separation of variables ây

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A: Given as, x¨= y˙ -1 . , y¨=-x-2      u=x˙ and v=y˙       u˙=x¨  v˙=y¨

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Q: 2. Find the differential equation of the family of curves as described below. a. Family of circles…

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Q: Obtain the general solution of the second order ordinary differential equa- tion y" +y= sec"(1)

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

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Q: from the partial differential equation eliminating the constant from (x-a)2 +(y-b)2 =z2 cot 2alfa,…

A: In this we make two equation by finding Partial derivative of equation w.r.t. x and w.r.t. y  With…

Q: from the partial differential equation eliminating the constant from (x-a)2+(y-b)2=z2 cot 2alfa,…

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Q: By using separation of variables u(x, t) = X(x)T(t), break the partial differ- ential equation ди +…

A: ∂2u∂t2 +∂u∂t +u=4∂2u∂x2            (1) To solve : Given partial differential equation by method of…

Q: 1. Consider the ordinary differential equation = (1-x-¹)y, with the initial values x = 1, y = 1.…

A: The fourth order Runge-Kutta method uses the following formulas to approximate the values of y at…

Q: 9. The characteristics of the partial differential equation *3 = 0 ду a əx dy +2- дх ду + cos? when…

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Q: Determine a region of the ty-plane for which the given differential equation would have a unique…

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Q: Q /Find the solution for the partial differential equation using Lagrange method az az + - ax = 2y…

A: We have the partial differential equation 2∂z∂x+∂z∂y=2y , where zx,0=cos3x If we have a partial…

Q: Use variation of parameters to to find the general solution of the non-homogeneous Euler-Cauchy…

A: To Determine :-  Use variation of parameters  to find the general solution of the non-homogeneous…

Q: form the partial differential equation by eliminating the arbitrary function from z=xy+f(x2+y2)

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Q: (a) Form a partial differential equation by eliminating the arbitrary functions f and g from z =…

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Q: Show that the solution of the differential equation (1–x*) = 2x(1+ y). dx 1+x given that y=1 when…

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Q: Find all the solutions of partial differential equation 25u ôx? by variable separable %3D method.…

A: All the solution of the partial differentilal equation is(1) u(x,t) =(Ax+B)(Ct+D)    (2)…

Q: obtain in alinear differential eqaution with real, constant coefficients that is satisfied by the…

A: The solution of the problem is given in the next step.

Q: Eliminate the arbitrary functions and hence obtain the partial differential equations:   z = f(x *…

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Q: Eliminate arbitrary constant from z=(x-a^2)+(y-b^2) to from the partial differential equation

A: Given z=x-a2*y-b2Hence number arbitary constant is 2 and number of independent variable is 2 . So…

Q: (y') ² + (x-2x^-½) y'+ x^-1 - x^½= 0

A: As per the company rule, we are supposed to solve one problem. Therefore kindly repost the second…

Q: 7. Find the differential dy of the function y = x (1-cos(x)). If the error in x is ", find the error…

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Q: 18. The linear partial differential equation yu + 2xu with variable coefficients is best classified…

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Q: 9. Form the differential equation of the three-parameter family of conics y = ae* + be2x + ce¬3x…

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Q: c) Find the product solutions for the differential equation Ux = -3uyy using separation %3D of…

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Q: Verify that the indicated function is an explicit solution of the given differential equation.…

A: Calculation shown in the solution is correct , i am providing you the  answer for each boxes…

Q: Differential equation in Q3(a) is added with 4e* and 10e* as Y, =6y, + y; +4e* Y, =5y, +2y; +10e"…

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Q: The linear and homogeneous differential equation of order 2 with coefficients in the range (a, b) is…

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Q: 2(a) Given that f(x, y) = 6x²y3 – cosx + 5y – siny + 10x, establish the fact that, the order in…

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Q: Consider the nonlinear time-dependent ordinary differential equation (ODE) y '(t) = y ^2 (t)+…

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Q: 6. Use separation of variables to find product solution of u(x, y) for the partial differential…

A: Given,            ∂2u∂y2=∂u∂x+xu                        (1)

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Q: Use centered finite differences to solve the ordinary differential equation for 0≤x≤6 d² u du +3…

A: We will use the basic knowledge of ordinary differential calculus to answer this question.

Q: Q.2 (a) Form Partial differential equation from z = ax² + by?

A: the given equation is z = ax2 + by2 .......(1)

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Q: Suppose g: IR →R has 3 distinct roots. How many distinct piecewise-constant solutions does the…

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Q: 2. Use the underermined coefficients method to find the goneal Scution of the differential…

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Q: 5. Determine the differential equation of minimum possible order linear homogeneous differential…

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Q: x(1+ y³)dy + ydx = 0 ;y(1) = 1 Ans: In(xy)³ + y3 = 1

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