What is the solution for 49y^{''}-70y^'+25y=0,y(0)=2,y^'(0)=3 ?

The solution for 49y^{''}-70y^'+25y=0,y(0)=2,y^'(0)=3 is y=2e^{(5t)/7}+(11e^{(5t)/7}t)/(7)

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49y^{''}-70y^'+25y=0,y(0)=2,y^'(0)=3

49 y^{^{''}} - 70 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = 3

y = 2 e^{\frac{5 t}{7}} + \frac{11 e ^{\frac{5 t}{7}} t}{7}

Solution steps

49 y^{''} (t) - 70 y^{'} (t) + 25 y = 0

Solve linear ODE:

y = 2 e^{\frac{5 t}{7}} + \frac{11 e ^{\frac{5 t}{7}} t}{7}

y = 2 e^{\frac{5 t}{7}} + \frac{11 e ^{\frac{5 t}{7}} t}{7}

What is the solution for 49y^{''}-70y^'+25y=0,y(0)=2,y^'(0)=3 ?
The solution for 49y^{''}-70y^'+25y=0,y(0)=2,y^'(0)=3 is y=2e^{(5t)/7}+(11e^{(5t)/7}t)/(7)