Question

The differential equation y′′=0y′′=0 has one of the following two parameter families as its general solution: yyyy=C1ex+C2e−x=C1cos(x)+C2sin(x)=C1tan(x)+C2sec(x)=C1+C2xy=C1ex+C2e−xy=C1cos⁡(x)+C2sin⁡(x)y=C1tan⁡(x)+C2sec⁡(x)y=C1+C2x Find the solution such that y(0)=6y(0)=6 and y′(0)=9y′(0)=9.

Answer 1

Answer:

$y(x)=6+9x$

Step-by-step explanation:

Given differential equation, $y''=0$

Characteristic equation is given by $m^2=0$

$\Rightarrow m=0,0$.

Differential equation have repeated roots and solution of differential equation is $y(x)=C_1+C_2x$.............................(1)

Initial conditions are $y(0)=6,y'(0)=9$

Plugging first condition in equation (1),

$6=C_1+C_2(0)$

$C_1=6$

Equation (1) becomes

$y(x)=6+C_2x$............................(2)

differentiate equation (2) with respect to 'x',

$y'(x)=C_2$

Plugging second condition,

$C_2=9$

Hence, $y(x)=6+9x$