Given that y, = 1, y2 = x2,y3 = e* are solutions of a third order differential equation (E). Then Wronskian W of y,, y2, yzis: 2e^x (x-1) None of them 2xe^x

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Q: (b) Form the differential equation by eliminating the arbitrary constants a,b from y = aez + be 8z

A: Differentiate twice with respect to x then we get the answer

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Q: 4. Show that both x₁ (t) = et cost and x2(t) = et sint are solutions to the second-order…

A: To show that both x1t=e-t cos t, and  x2t=e-t sin tare solutions to the second‐order differential…

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A: Consider the given equation. mdvdt=mg-kv Further, simplify and make for integration.…

Q: For this question, please consider the nonlinear partial differential equation ux3 + uy3 = u2.…

A: Given : ux3+uy3=u2 To Find : (i)complete solution                (ii) ux ,0 =x+1327

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Q: Consider the differential equation 1 y' = x – 2 with the initial condition y (xo) = = Yo What must…

A: We are given : y'=y-13x-2⇒dydx=y-13x-2⇒dyy-13=dxx-2Now, we will Integrate both…

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A: Given statement is

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A: Equation of normal at the point P(x,y) to the curve is Y-y=-dxdy(X-x). ⇒X=x+ydydx Thus,…

Q: 2. Consider the differential equation y' -()y = 2+G) t If y(0) = yo, find the particular solution to…

A: Explanation of the solution is given below...

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Q: 1. (2x + y – 1)dy + (4x + 2y – 3)dx = 0; when x = 1, y = 2

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Q: -) Solve the following partial differential equation us ing direct integration: a²u = cos (x +y) дх…

A: Topic:- application of integration

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A: considergiven differential equationdydx-y=xdydx=x+y; y0=0h=0.1

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A: We will show that the given differential equation describing such curve is correct and will find the…

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Q: If the family of curve has 3 arbitrary constants then the corresponding differential equation is a)…

A: See solution below

Q: The function y = x2 In x is a solution to the differential equation 4x² y" + y = 0. First, use…

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Q: Suppose sinh 2x, y2 = 6x, y3 = cos 2x are solutions of a linear homogeneous differential equation…

A: To find the differential equation :-

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A: We are given the second order linear differential equation. y"=x+y. or  d2ydx2=x+y....(1) We need do…

Q: الموافق Find the general integra) of the differential equations with dottedf v ariables : ト 3) (++y)…

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Q: Suppose y₁ = sinh 2x, y2 = 6x, y3 = cos 2x are solutions of a linear homogeneous differential…

A: To find the differential equation :-

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

A: Given : PDE ∂2u∂y2=∂u∂x+xu To find : product solution of ux, y using separation of variables

Q: Use Teller's method to Solve the differential equation y-X JJ when h=0-2 s y(1)=2 Use The fifth rank…

A: We can solve this using Taylor method

Q: Define the term homogeneous first order ordinary differential equation.  Hence solve x2y' + xy = x2…

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Q: Determine the general solution of the given differential equation that is valid in any interval not…

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Q: determine the general solution of given non-homogeneous differential equations using different…

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Q: ху' — 2у + 2 y — хе*

A: The Cauchy-Euler second order nonhomogeneous differential equation is ax2y''+by'+cy=h(x). Where a, b…

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