| Exam Board | Edexcel |
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| Module | FP2 (Further Pure Mathematics 2) |
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| Topic | Second order differential equations |
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3. (a) Show that \(y = \frac { 1 } { 2 } x ^ { 2 } \mathrm { e } ^ { x }\) is a solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - 2 \frac { \mathrm {~d} y } { \mathrm {~d} x } + y = \mathrm { e } ^ { x }$$
(b) Solve the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - 2 \frac { \mathrm {~d} y } { \mathrm {~d} x } + y = \mathrm { e } ^ { x }$$
given that at \(x = 0 , y = 1\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2\).
[0pt]
[P4 January 2002 Qn 7]