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प्रश्न
The general solution of a differential equation of the type `dx/dy + P_1 x = Q_1` is ______.
पर्याय
`y e^(intP_1 dy) = int(Q_1 e^(intP_1 dy)) dy + C`
`y . e^(intP_1 dx) = int(Q_1 e^(intP_1 dx)) dx + C`
`x e^(intP_1 dy) = int(Q_1 e^(intP_1 dy)) dy + C`
`xe^(intP_1 dx) = int(Q_1 e^(intP_1 dx)) dx + C`
उत्तर
The general solution of a differential equation of the type `dx/dy + P_1 x = Q_1` is `underline(x e^(int P_1 dy) = int (Q_1e^(int P_1dy)) dy + C)`.
Explanation:
Given the differential equation
`dx/dy + P_1 x = Q_1`
where P1 and Q1 are functions of y.
∴` I.F. = e^(int P_1dy)`
Hence, the required solution
`x * e^(P_1dy) = int (Q_1 xx e^(int P_1 dy))dy + C`
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