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[SOLVED] 1.3.10 Verify the following given functions is a solution of the differential equation

karush

Well-known member
Jan 31, 2012
3,004
$\textsf{ Verify the following given functions is a solution of the differential equation}\\ \\$
$y''''+4y'''+3y=t\\$
$y_1(t)=t/3$
\begin{align*}
(t/3)''''+4(t/3)'''+(t/3)&=t\\
0+0+t&=t
\end{align*}
$y_2(t)=e^{-t}+t/3$
\begin{align*}
(e^{-t}+t/3)''''+4(e^{-t}+t/3)'''+3(e^{-t}+t/3)&=t\\
e^{-t}-4e^{-t}+3e^{-t}+3e^{-t}+t&=t\\
t&=t
\end{align*}

so is it Raj now?

$$\tiny{\textsf{Elementary Differential Equations and Boundary Value Problems}}$$
 

Rido12

Well-known member
MHB Math Helper
Jul 18, 2013
715
A bunch of typos but it's correct. First one it's $3 \cdot (t/3)$, and second one you copied $3e^{-t}$ twice.
 

karush

Well-known member
Jan 31, 2012
3,004
$\textsf{ Verify the following given functions is a solution of the differential equation}\\ \\$
$y''''+4y'''+3y=t\\$
$y_1(t)=t/3$
\begin{align*}
(t/3)''''+4(t/3)'''+3(t/3)&=t\\
0+0+t&=t
\end{align*}
$y_2(t)=e^{-t}+t/3$
\begin{align*}
(e^{-t}+t/3)''''+4(e^{-t}+t/3)'''+3(e^{-t}+t/3)&=t\\
e^{-t}-4e^{-t}+3e^{-t}+t&=t\\
t&=t
\end{align*}