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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.

Respuesta :

Answer:

[tex]y(x)=6+9x[/tex]

Step-by-step explanation:

Given differential equation, [tex]y''=0[/tex]

Characteristic equation is given by [tex]m^2=0[/tex]

[tex]\Rightarrow m=0,0[/tex].

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

Initial conditions are [tex]y(0)=6,y'(0)=9[/tex]

Plugging first condition in equation (1),

[tex]6=C_1+C_2(0)[/tex]

[tex]C_1=6[/tex]

Equation (1) becomes

[tex]y(x)=6+C_2x[/tex]............................(2)

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

[tex]y'(x)=C_2[/tex]

Plugging second condition,

[tex]C_2=9[/tex]

Hence, [tex]y(x)=6+9x[/tex]

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