#### Question

The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is

(a) \[y e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\]

(b) \[y e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\]

(c) \[x e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\]

(d) \[x e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\]

#### Solution

\[\left( c \right) x e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\]

We have,

\[\frac{dx}{dy} + P_1 x = Q_1\]

Comparing with the equation \[\frac{dx}{dy} + Px = Q\], we get

P = P

Q = Q

The general solution of the equation \[\frac{dx}{dy} + Px = Q\] is given by \[x e^\int Pdy = \int\left\{ Q e^\int Pdy \right\}dy + C\] ...(1)

Putting the value of P and Q in (1), we get

Comparing with the equation \[\frac{dx}{dy} + Px = Q\], we get

P = P

_{1}Q = Q

_{1}The general solution of the equation \[\frac{dx}{dy} + Px = Q\] is given by \[x e^\int Pdy = \int\left\{ Q e^\int Pdy \right\}dy + C\] ...(1)

Putting the value of P and Q in (1), we get

\[x e^\int Pdy = \int\left\{ Q e^\int Pdy \right\}dy + C\]

Is there an error in this question or solution?

Solution The General Solution of a Differential Equation of the Type D X D Y + P 1 X = Q 1 is (A) Y E ∫ P 1 D Y = ∫ { Q 1 E ∫ P 1 D Y } D Y + C (B) Y E ∫ P 1 D Y = ∫ { Q 1 E ∫ P 1 D Y } D Y + Concept: General and Particular Solutions of a Differential Equation.