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Solve Differential Equationdifferential equation using a integral form Boundary Conditionboundary condition

I have a second order differential equation and I want to solve it analytically (DSolve) and numerically (NDSolve) with following boundary conditions.

y''[x] - y[x] == (x^2) 

B.CBoundary conditions:

y[0] == 1
Integrate[y[x], {x, 0, 2}] == 5

How can I implement an integral form B.C.boundary condition for solving this differential equation?

Solve Differential Equation using a integral form Boundary Condition

I have a second order differential equation and I want to solve it analytically (DSolve) and numerically (NDSolve) with following boundary conditions.

y''[x] - y[x] == (x^2) 

B.C:

y[0] == 1
Integrate[y[x], {x, 0, 2}] == 5

How can I implement integral form B.C. for solving differential equation?

Solve differential equation using a integral form boundary condition

I have a second order differential equation and I want to solve it analytically (DSolve) and numerically (NDSolve) with following boundary conditions.

y''[x] - y[x] == (x^2) 

Boundary conditions:

y[0] == 1
Integrate[y[x], {x, 0, 2}] == 5

How can I implement an integral form boundary condition for solving this differential equation?

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