| Exam Board | Edexcel |
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| Module | FP2 (Further Pure Mathematics 2) |
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| Year | 2003 |
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| Session | June |
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| Topic | First order differential equations (integrating factor) |
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6. (a) Using the substitution \(t = x ^ { 2 }\), or otherwise, find
$$\int x ^ { 3 } \mathrm { e } ^ { - x ^ { 2 } } \mathrm {~d} x$$
(b) Find the general solution of the differential equation
$$x \frac { \mathrm {~d} y } { \mathrm {~d} x } + 3 y = x \mathrm { e } ^ { - x ^ { 2 } } , \quad x > 0$$