SOLUTION: 1). The equation y^“+y^'-2y=5 is called a differential equation because it involves the unknown function y and its derivative y^' and y^“. Find the constants A, B, C such that the

Algebra ->  Trigonometry-basics -> SOLUTION: 1). The equation y^“+y^'-2y=5 is called a differential equation because it involves the unknown function y and its derivative y^' and y^“. Find the constants A, B, C such that the       Log On


   

Question 862277: 1). The equation y^“+y^'-2y=5 is called a differential equation because it involves the unknown function y and its derivative y^' and y^“. Find the constants A, B, C such that the function y=Ax^2+Bx+C satisfies the equation.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
dy%2Fdx=2Ax%2BB
d%28dy%2Fdx%29%2Fdx=2A
So then,
2A%2B2Ax%2BB-2%28Ax%5E2%2BBx%2BC%29=5
2A%2B2Ax%2BB-2Ax%5E2-2Bx-2C=5
-2Ax%5E2-2Bx%2B2Ax%2B2A-2C=5
%28-2A%29x%5E2%2B2%28A-B%29x%2B%282A%2BB-2C%29=5
So comparing terms right hand side and left hand side,
x%5E2 term
-2A=0
A=0
.
.
x term
2%28A-B%29=0
2%280-B%29=0
B=0
and finally,
2A%2BB-2C=5
2%280%29%2B0-2C=5
-2C=5
C=-5%2F2
So,
highlight%28y=-5%2F2%29