What is the solution for y^{''}-5y^'=3cos(x) ?

The solution for y^{''}-5y^'=3cos(x) is y=c_{1}e^{5x}+c_{2}-15/26 sin(x)-3/26 cos(x)

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y^{''}-5y^'=3cos(x)

y^{^{''}} - 5 y^{^{'}} = 3 cos (x)

y = c_{1} e^{5 x} + c_{2} - \frac{15}{26} sin (x) - \frac{3}{26} cos (x)

Solution steps

y^{''} (x) - 5 y^{'} (x) = 3 cos (x)

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} - \frac{15}{26} sin (x) - \frac{3}{26} cos (x)

y = c_{1} e^{5 x} + c_{2} - \frac{15}{26} sin (x) - \frac{3}{26} cos (x)

What is the solution for y^{''}-5y^'=3cos(x) ?
The solution for y^{''}-5y^'=3cos(x) is y=c_{1}e^{5x}+c_{2}-15/26 sin(x)-3/26 cos(x)