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

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

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

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

y = \frac{x ^{3}}{6} - \frac{x}{6}

Solution steps

y^{''} (x) = x

Solve

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

Solve

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

Apply initial conditions:

y = \frac{x ^{3}}{6} - \frac{x}{6}

y = \frac{x ^{3}}{6} - \frac{x}{6}

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