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## eshen Group Title 1. Consider the differential equation x4y′′ − x3y′ = 8. (b) Show that Ax^2 + 1 + B is a solution to the equation, where A and B are x^2 ￼constants. one year ago one year ago

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1. enano9314

I would make the coefficient in front of the y'' a 1, and then use u=y' to reduce it to a first order differential equation. And then use a simple integrating factor technique

2. RolyPoly

What is part (a)?

3. RolyPoly

One way I can think of is to make the left side looks like the Cauchy-Euler equation.. $x^4y′′ − x^3y′ = 8$$x^2y′′ − xy′ = \frac{8}{x^2}$Set the left =0 $\lambda (\lambda -1) - \lambda = 0$$\lambda = 0, 2$$y_c = c_1x^2+c_2$And then find the particular solution.

4. eshen

Thanks a bunch!