7 Find the particular solution of the differential equation
$$49 \frac { \mathrm {~d} ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 14 \frac { \mathrm {~d} y } { \mathrm {~d} x } + y = 49 x + 735$$
given that when \(x = 0 , y = 0\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\).
7 Find the particular solution of the differential equation
$$49 \frac { \mathrm {~d} ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 14 \frac { \mathrm {~d} y } { \mathrm {~d} x } + y = 49 x + 735$$
given that when $x = 0 , y = 0$ and $\frac { \mathrm { d } y } { \mathrm {~d} x } = 0$.\\
\hfill \mbox{\textit{CAIE FP1 2018 Q7}}