hello guys, please help me with my assignment. thank you so much.
1. eliminate the arbituary constant on this eqn. y=C1e^2x+C2e^x+C3
2. evaluate and find the general solution of this eqn.
a. x sqrt1+y^2 dx - y sqrt1+x^2 dy=0
b. 2ycosxdx+3sinxdy = 0
thank you so much. god bless! ^_^
Problem 1
$y =C_1 e^{2x} + C_2 e^x + C_3$ ← eq (1)
There are 3 arbitrary constants C1, C2, and C3, hence, we can differentiate eq (1) up to three times.
$y' = 2C_1 e^{2x} + C_2 e^x$ ← eq (2)
$y'' = 4C_1 e^{2x} + C_2 e^x$ ← eq (3)
$y''' = 8C_1 e^{2x} + C_2 e^x$ ← eq (4)
eq (3) - eq(2)
$y'' - y' = 2C_1 e^{2x}$ ← eq (5)
eq (4) - eq(3)
$y''' - y'' = 4C_1 e^{2x}$ ← eq (6)
eq (6) - 2×eq (5)
$(y''' - y'') - 2(y'' - y') = 0$
$y''' - y'' - 2y'' + 2y' = 0$
$y''' - 3y'' + 2y' = 0$ answer
Add new comment