Question

3. State whether the following statements are true or false? You don't need to explain your answers 1. The functions yı = sin(t) and y2 = sin(21) are linearly independent for all values of t. [2pts) 2. Laplace Transform C is a linear operator. [2pts) e24 3. If A = then et [2pts) = ( 1), ti 4. If we use method of undetermined coefficients to find the particular solution Y (t) for this differential equation y"+y=sint, then Y (t) = Asint + B cost [2pts] 5. If yı and ya are fundamental solutions of a second order differential equation y" +ay'+b= 0, then any other solution y(t) can be represented using y(t) = cıyı + c2y2. Here, a,b,c1.c are constants. [2pts]

Answer 1

sir if any mistake plz comment

3 6 yos sin(t) & 4 -519(24) Ws 810) S10 (4) Cost) 2005(24) 2 s19 (+) Cus(et) - Cojoj312121 fo (TRUE so Linearly Independent 5 ③ [a fet + b901] L[fil] +6 LC90] Y [che]CL[+01 SO Linear (TRUE) At H as c (31) 4:16: [*] -(TRUE bolt 10 yl ty asints tęlost) Yes - Sholt) FALSE Ypt's at (sint tcost) . Yo A SINOJ + BC SHJ particular solution (true = This is compejmentady solution). gll taylfb so fundamental solution 4,8% 15 .: YHs gyit 6 Yeni 7 TRUE