Question

At least one of the answers above is NOT correct. Find the function $y_1$ of $t$ which is the solution of $121y'' - 154y' + 13y = 0$ with initial conditions $y_1(0) = 1$, $y_1'(0) = 0$. $y_1 = (1 - (13/12))e^{(13t/11)} + (13/12)e^{t/11}$ Find the function $y_2$ of $t$ which is the solution of $121y'' - 154y' + 13y = 0$ with initial conditions $y_2(0) = 0$, $y_2'(0) = 1$. $y_2 = (11/12)e^{(13t/11)} - (11/12)e^{t/11}$ Find the Wronskian $W(t) = W(y_1, y_2)$. $W(t) = (-12/11)e^{(14t/11)}$ Remark: You can find $W$ by direct computation and use Abel's theorem as a check. You should find that $W$ is not zero and so $y_1$ and $y_2$ form a fundamental set of solutions of $121y'' - 154y' + 13y = 0$.

          At least one of the answers above is NOT correct.
Find the function $y_1$ of $t$ which is the solution of
$121y'' - 154y' + 13y = 0$
with initial conditions $y_1(0) = 1$, $y_1'(0) = 0$.
$y_1 = (1 - (13/12))e^{(13t/11)} + (13/12)e^{t/11}$
Find the function $y_2$ of $t$ which is the solution of
$121y'' - 154y' + 13y = 0$
with initial conditions $y_2(0) = 0$, $y_2'(0) = 1$.
$y_2 = (11/12)e^{(13t/11)} - (11/12)e^{t/11}$
Find the Wronskian
$W(t) = W(y_1, y_2)$.
$W(t) = (-12/11)e^{(14t/11)}$
Remark: You can find $W$ by direct computation and use Abel's theorem as a check. You should find that $W$ is not zero and so $y_1$ and $y_2$ form a
fundamental set of solutions of
$121y'' - 154y' + 13y = 0$.

At least one of the answers above is NOT correct.
Find the function y1 of t which is the solution of
121y” - 154y' + 13y = 0
with initial conditions y1(0) = 1, y1'(0) = 0.
y1 = (1 - (13/12))e^(13t/11) + (13/12)e^t/11
Find the function y2 of t which is the solution of
121y” - 154y' + 13y = 0
with initial conditions y2(0) = 0, y2'(0) = 1.
y2 = (11/12)e^(13t/11) - (11/12)e^t/11
Find the Wronskian
W(t) = W(y1, y2).
W(t) = (-12/11)e^(14t/11)
Remark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so y1 and y2 form a
fundamental set of solutions of
121y” - 154y' + 13y = 0.

Added by Charles A.

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