# [SOLVED]second order homogeneous equations with non constant coefficients

#### shorty

##### New member
I was given a question and i am really unsure how to go about solving it. it appears to be solveable using the characteristic equation and whatnot, however i have my coeffecients in terms of the independent variable. so i am confused. the question initially asked to compute the wronskian, and it gave the solutions, then it gives initial values to solve. There's where the confusion began. I'd be grateful for some guidance please.

Solve the initial value problem
$$\displaystyle 2t^2y''+3ty'-y= 0; y(1)=2, y'(1)=1$$, given that $$\displaystyle y_1(t)=\sqrt(t) \mbox{ and } y_2​(t)=\frac{1}{t}$$

The question also asked to use the Wronskian to show that the two solutions are linearly independent, then said, hence, solve the ivp (given above). I calculated the Wronskian to be $$\displaystyle \frac{-3 \sqrt{t}}{2t^2​}$$

(These delimiters are not working for me, they are doing their own thing. quite annoying. )

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#### dwsmith

##### Well-known member
I was given a question and i am really unsure how to go about solving it. it appears to be solveable using the characteristic equation and whatnot, however i have my coeffecients in terms of the independent variable. so i am confused. the question initially asked to compute the wronskian, and it gave the solutions, then it gives initial values to solve. There's where the confusion began. I'd be grateful for some guidance please.

Solve the initial value problem
$$2t2y''+3ty'-y= 0; y(1)=2, y'(1)=1, given that y1(t)=\sqrt(t) and y2​(t)=\frac{1}{t} The question also asked to use the Wronskian to show that the two solutions are linearly independent, then said, hence, solve the ivp (given above). I calculated the Wronskian to be \frac{-3 \sqrt{t}}{2t2​}$$

(These delimiters are not working for me, they are doing their own thing. quite annoying. )

#### dwsmith

##### Well-known member
isn't that what i've done?
I don't know what is wrong with it but I can't even copy and change it correctly.

#### shorty

##### New member
well your 'iput' came out as Math. same thing was happening to part of what i was writing, and not the actual math that i wanted in the latex.

$$2t2y''+3ty'-y= 0; y(1)=2, y'(1)=1, \ \text{given that} \ y1(t)=\sqrt(t) and y2​(t)=\frac{1}{t}$$

I put $$at the end of this math. #### dwsmith ##### Well-known member well your 'iput' came out as Math. same thing was happening to part of what i was writing, and not the actual math that i wanted in the latex.$$
2t^2y''+3ty'-y= 0; y(1)=2, y'(1)=1, \ \text{given that} \ y_1(t)=\sqrt{t} and y_2(t)=\frac{1}{t}
$$Will this work? #### shorty ##### New member neither. i tried that too. is it me? i just restarted my browser and getting the same thing. the thing is when i started writing the question i previewed just as i started and the math came out fine, then when i added more it messed up and that was it.$$
2t^2y''+3ty'-y= 0; y(1)=2, y'(1)=1, given that y_1(t)=\sqrt(t) and y_2(t)=\frac{1}{t}