What is the solution for y^{''}=6x,y(0)=1,y^'(0)=-1 ?

The solution for y^{''}=6x,y(0)=1,y^'(0)=-1 is y=x^3-x+1

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y^{''}=6x,y(0)=1,y^'(0)=-1

y^{^{''}} = 6 x, y (0) = 1, y^{^{'}} (0) = - 1

y = x^{3} - x + 1

Solution steps

y^{''} (x) = 6 x

Solve

y^{''} (x) = 6 x : y^{'} (x) = 3 x^{2} + c_{1}

Solve

y^{'} (x) = 3 x^{2} + c_{1} : y = x^{3} + c_{1} x + c_{2}

Apply initial conditions:

y = x^{3} - x + 1

y = x^{3} - x + 1

What is the solution for y^{''}=6x,y(0)=1,y^'(0)=-1 ?
The solution for y^{''}=6x,y(0)=1,y^'(0)=-1 is y=x^3-x+1