Without using de-solver, solve the IVP xy’+ y = 3x, y(1) = 0. Write your answer in explicit solution form.

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Q: Find a solution to the initial value problem, y" + 6x = 0, y(0) = -2, y (0) = -5.

A: y'' +6x=0⇒y'' =-6xIntegrating both sides,⇒y'=-3x2+c1Integrating both sides,⇒y=-x3+c1x+c2 We have…

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Q: Q2/ Solve the differential equation by using the appropriate method y' = (y + 4x)2

A: Formulas of the differentiation and integration ddxxn=nxn-1∫xndx=xn+1n+1+C∫1x2+a2dx=1atan-1xa+C

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Q: 35. (2v3 3)dx + 3xv²dv = 0 – x

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Q: y" = 12x² %3D

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Q: Find the general solution for y''=2t+3 by direct integration and by the method of undetermied…

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Q: Use the Method of Undetermined Coefficients to solve the Initial Value Problem y" + 2y'+ y = 3t ,…

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Q: Find a solution to the initial value problem, y′′+6x=0, y(0)=−4, y′(0)=3   y =

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Q: a. the root of the given nonlinear equation on its 16th iteration?

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Q: = (+ Use the fact that i and -i = to solve the differential equation dx4 + y = 0.

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A: We will find out the required solution for the given differential equation.

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Q: Some initial value problems do not have unique solutions صواب ihi

A: Yes statement is true: y(t)=0 for t∈[0,1] and y(t)=(t−1)^2 for t≥1.

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Q: ydx – xdy Solve the differential equation 2xdx=- x2. + y? by forming integrable combinations.

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Q: Suppose we are given y1(x) and y2(x) (with y1 ≠ y2), which are two different solutions of a…

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Q: of Solve the initial value problem 3D6 xdy + dy=ydx, yca) =6 t. %31

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A: We find a differential equation whose general solution is y=c1e6t+c2e-3t.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.