Find a solution to the differential equation y''-y=sinh x

Here we solve for y(x) from a second order linear differential equation.
y''(x)-y(x)=sinh(x)
here we find the homogeneous solution setting y''-y=0.
Then we find a particular solution but setting sinh(x) to its exponential identity of 1/2(e^x-e^-x) .
That way we can use a system of corresponding coefficients to solve.
The solution is the homogeneous solution plus the particular solution.
y(x) is our dependent variable as it depends on x.
x is our independent variable

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#calculus
#calculusofvariations
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#multivariable
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