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5. Consider the IVP t2y" + ty' 4y = 0, 9(1) = 0,y (1) = 1 Classify the differential equationby order; linear_ nonlinear; homogenious /nonhomogenious. (3 p...

Question

5. Consider the IVP t2y" + ty' 4y = 0, 9(1) = 0,y (1) = 1 Classify the differential equationby order; linear_ nonlinear; homogenious /nonhomogenious. (3 pts) () Confirm that the set of vectors {t- 2, t2} is a basis of the solution space: (10 pts) (c) Solve the IVP (5 pts)

5. Consider the IVP t2y" + ty' 4y = 0, 9(1) = 0,y (1) = 1 Classify the differential equationby order; linear_ nonlinear; homogenious /nonhomogenious. (3 pts) () Confirm that the set of vectors {t- 2, t2} is a basis of the solution space: (10 pts) (c) Solve the IVP (5 pts)



Answers

Determine which of the following sets of vectors is a basis for the solution space to the differential equation $x^{2} y^{\prime \prime}-3 x y^{\prime}+4 y=0$ on the interval $(0, \infty)$ $S_{1}=\left\{x^{2}\right\}, S_{2}=\left\{x^{2}, x^{2} \ln x\right\}, S_{3}=\left\{2 x^{2}, 3 x^{2} \ln x\right\}$ $S_{4}=\left\{x^{2}(2+3 \ln x), x^{2}(2-3 \ln x)\right\}$

So the answer for the given question is why Dash equals two c one year to the poverty Bless CEO and took twice Steve Less, too. Wire Nash. One physicals to see one less force Ito see one he less fourth Cito resembles to one. Luckily, with second equation, subtract one from no that this Sciutto will be four to minus one on C one will be equal to five by he. Therefore, the solution will be via calls to five by he and career to the power T minus is where minus to B minus two. Thank you.

Mm. Were given this differential equation D. V D. T. Which is defined as three T squared -2 T. Plus one. So the first thing I would do is find a anti derivative that works. So that would be adding one to the expo and divide by your new exponent, adding one to your exponents, divide by your new expert. And this should make sense because the derivative of T cubed is three T square. The derivative of T squared is two T. And the derivative of tea is one. But don't forget about plus C. Because we also have this initial condition that when T. Is one B. Is five. So what I need to do is go to all of my teas and plug in one or one to any powers just one. I'm going to get a b. value of five. So as I reduce this just a little bit like one minus one is zero plus one is one. Maybe I'll just do this and subtract 1/5 minutes. One is four. Is your C. Value. Well now I know the exact answer that the best or the only correct answer. The one who's derivative gives me the differential equation and hits the point 15 Has to have a c. value of four. Um And this is it. It's the only correct answer.


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