What is the solution for y^{''}-0.2y^'+0.01y=0,y(0)=14,y^'(0)=b ?

The solution for y^{''}-0.2y^'+0.01y=0,y(0)=14,y^'(0)=b is y=14e^{t/(10)}+(b-7/5)e^{t/(10)}t

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y^{''}-0.2y^'+0.01y=0,y(0)=14,y^'(0)=b

y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 14, y^{^{'}} (0) = b

y = 14 e^{\frac{t}{10}} + (b - \frac{7}{5}) e^{\frac{t}{10}} t

Solution steps

y^{''} (t) - 0.2 y^{'} (t) + 0.01 y = 0

Solve linear ODE:

y = 14 e^{\frac{t}{10}} + (b - \frac{7}{5}) e^{\frac{t}{10}} t

y = 14 e^{\frac{t}{10}} + (b - \frac{7}{5}) e^{\frac{t}{10}} t

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x \to 0 lim (\frac{a x - a ln ( x + 1 )}{x ln ( x + 1 )})

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What is the solution for y^{''}-0.2y^'+0.01y=0,y(0)=14,y^'(0)=b ?
The solution for y^{''}-0.2y^'+0.01y=0,y(0)=14,y^'(0)=b is y=14e^{t/(10)}+(b-7/5)e^{t/(10)}t