Question

Solve the differential equation: $2e^{x+2y}dx-3dy=0$

Answer 1

Solution:

1) separate the variables

$2e^{x+2y}dx-3dy=0 \\ \\ 2 {e}^{x} {e}^{2y} dx - 3dy = 0 \\ \\ 2 {e}^{x} dx = \frac{3}{ {e}^{2y} } dy \\ \\ 2 {e}^{x} dx = 3{e}^{ - 2y} dy$
2) integrate both side

$2\int {e}^{x} dx = 3\int{e}^{ - 2y} dy \\ \\ 2 {e}^{x} = \frac{ - 3}{2} {e}^{ - 2y} + c$
3) put terms of y in LHS and rest all to RHS

$4 {e}^{x} = { - 3}{e}^{ - 2y} +2 c \\ \\ - 3 {e}^{ - 2y} = 4 {e}^{x} - 2c \\ \\ or \\ \\ 3 {e}^{ - 2y} = 2c - 4 {e}^{x}$

Answer 2

Answer:

here is the answer as per the textbook