The general solution of the differential equation dx = e x + y is e x + e - y = C e x + e y = C e - x + e y = C e - x + e - y = C

Option a is correct dx = e x e y e y = e x dx … (1) Integrating (1) both sides, we get - e - y + C = e x + e - y = C , is the required general solution. Exercise-9.5

Differential Equations — Class 12 Maths Solution

ncert exercise SA NCERT Ex.9.4,Q.23,Page 397

Question

The general solution of the differential equation $\cfrac{{dy}}{{dx}} = {e^{x + y}}$ is

• ${e^x} + {e^{ - y}} = C$

• ${e^x} + {e^y} = C$

• ${e^{ - x}} + {e^y} = C$

• ${e^{ - x}} + {e^{ - y}} = C$

Step-by-step Solution

Option a is correct

$\cfrac{{dy}}{{dx}} = {e^x}{e^y} \Rightarrow \cfrac{{d.y}}{{{e^y}}} = {e^x}dx$

… (1)
Integrating (1) both sides,

we get
$- {e^{ - y}} + C = {e^x} \Rightarrow {e^x} + {e^{ - y}} = C$, is the required general solution.

Exercise-9.5

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