What is the solution for y^{''}-10y^'+21y=e^{7t},y(0)=0,y^'(0)=0 ?

The solution for y^{''}-10y^'+21y=e^{7t},y(0)=0,y^'(0)=0 is y=-1/16 e^{7t}+1/16 e^{3t}+(e^{7t}t)/4

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y^{''}-10y^'+21y=e^{7t},y(0)=0,y^'(0)=0

y^{^{''}} - 10 y^{^{'}} + 21 y = e^{7 t}, y (0) = 0, y^{^{'}} (0) = 0

y = - \frac{1}{16} e^{7 t} + \frac{1}{16} e^{3 t} + \frac{e ^{7 t} t}{4}

Solution steps

y^{''} (t) - 10 y^{'} (t) + 21 y = e^{7 t}

Solve linear ODE:

y = - \frac{1}{16} e^{7 t} + \frac{1}{16} e^{3 t} + \frac{e ^{7 t} t}{4}

y = - \frac{1}{16} e^{7 t} + \frac{1}{16} e^{3 t} + \frac{e ^{7 t} t}{4}

y^{^{''}} + 3 y = - 48 e^{3 x}

\frac{1}{6} y^{^{''}} + 6 y = 4 tan (6 t) - \frac{1}{2} e^{t}

y^{^{''''}} + 2 y^{^{''}} + y = 3 + cos (2 x)

y^{^{''}} + 16 y = - 16 sec (4 x)

x^{^{''}} + 16 x^{^{'}} + 80 x = e^{- 8 t}

What is the solution for y^{''}-10y^'+21y=e^{7t},y(0)=0,y^'(0)=0 ?
The solution for y^{''}-10y^'+21y=e^{7t},y(0)=0,y^'(0)=0 is y=-1/16 e^{7t}+1/16 e^{3t}+(e^{7t}t)/4