What is the solution for y^{''}-ay^'-by=0 ?

The solution for y^{''}-ay^'-by=0 is y=c_{1}e^{(t(a+sqrt(a^2+4b)))/2}+c_{2}e^{(t(a-sqrt(a^2+4b)))/2}

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y^{''}-ay^'-by=0

y^{^{''}} - a y^{^{'}} - b y = 0

y = c_{1} e^{\frac{t ( a + a ^{2} + 4 b )}{2}} + c_{2} e^{\frac{t ( a - a ^{2} + 4 b )}{2}}

Solution steps

y^{''} (t) - a y^{'} (t) - b y = 0

Solve linear ODE:

y = c_{1} e^{\frac{t ( a + a ^{2} + 4 b )}{2}} + c_{2} e^{\frac{t ( a - a ^{2} + 4 b )}{2}}

y = c_{1} e^{\frac{t ( a + a ^{2} + 4 b )}{2}} + c_{2} e^{\frac{t ( a - a ^{2} + 4 b )}{2}}

What is the solution for y^{''}-ay^'-by=0 ?
The solution for y^{''}-ay^'-by=0 is y=c_{1}e^{(t(a+sqrt(a^2+4b)))/2}+c_{2}e^{(t(a-sqrt(a^2+4b)))/2}