What is the solution for 10000y^{''}-81y^'=0,y(0)=8,y^'(0)=5 ?

The solution for 10000y^{''}-81y^'=0,y(0)=8,y^'(0)=5 is y=(8+49352/81)e^{(81t)/(10000)}-49352/81

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10000y^{''}-81y^'=0,y(0)=8,y^'(0)=5

10000 y^{^{''}} - 81 y^{^{'}} = 0, y (0) = 8, y^{^{'}} (0) = 5

y = (8 + \frac{49352}{81}) e^{\frac{81 t}{10000}} - \frac{49352}{81}

Solution steps

10000 y^{''} (t) - 81 y^{'} (t) = 0

Solve linear ODE:

y = (8 + \frac{49352}{81}) e^{\frac{81 t}{10000}} - \frac{49352}{81}

y = (8 + \frac{49352}{81}) e^{\frac{81 t}{10000}} - \frac{49352}{81}

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 8, y (1) = 0

\frac{d ^{2} y}{d x ^{2}} - \frac{11}{2} \frac{d y}{d x} + 6 y = 0

y^{^{'''}} - 27 y = 0

(D^{2} - 6 D + 9) y = 0

4 y^{^{''}} + 4 y^{^{'}} + 512 y = 0, y (0) = 0, y^{^{'}} (0) = 7

What is the solution for 10000y^{''}-81y^'=0,y(0)=8,y^'(0)=5 ?
The solution for 10000y^{''}-81y^'=0,y(0)=8,y^'(0)=5 is y=(8+49352/81)e^{(81t)/(10000)}-49352/81