I'm trying to solve a below ODE problem with TI-nspire cas:
$$ y''-4y'+3y=cos^2x $$
If I solve the above problem by hand (or using the wolfram alpha), I get the
$$ y=c_1e^x+c_2e^{3x}+\frac16-\frac{1}{130}(cos 2x+8sin2x) $$ However, when I solve this with Ti-nspire cas, gives the following answer: $$ y=c_1e^x+c_2e^{3x}+\frac{31}{195}-\frac{8sin(x)cos(x)}{65}+\frac{sin(x)^2}{65} $$ I type in the calculator as follows: $$ desolve(y''-4y'+3y=(cos(x))^2,x,y) $$ Is there any problem with my input? Or is the calculator failing to solve this?
I look forward to some help. Thanks.
$\endgroup$ 51 Answer
$\begingroup$Use the trigonometric identities $\cos(2x) = 1-2 \sin^2 x $ and $\sin(2x) = 2 \sin x \cos x$.
You can check your answer by plugging each solution into the original ODE and seeing if it is true.
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