What is the solution for 2y^{''}-13y^'+15y=0,y(0)=0,y^'(0)=17.5 ?

The solution for 2y^{''}-13y^'+15y=0,y(0)=0,y^'(0)=17.5 is y=5e^{5t}-5e^{(3t)/2}

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2y^{''}-13y^'+15y=0,y(0)=0,y^'(0)=17.5

2 y^{^{''}} - 13 y^{^{'}} + 15 y = 0, y (0) = 0, y^{^{'}} (0) = 17.5

y = 5 e^{5 t} - 5 e^{\frac{3 t}{2}}

Solution steps

2 y^{''} (t) - 13 y^{'} (t) + 15 y = 0

Solve linear ODE:

y = 5 e^{5 t} - 5 e^{\frac{3 t}{2}}

y = 5 e^{5 t} - 5 e^{\frac{3 t}{2}}

θ^{^{''}} (t) + \frac{9. 8 ^{2}}{80} θ (t) = 0

\frac{( \frac{d ^{2} f}{d x ^{2}} )}{f ( x )} = 1

y^{^{''}} = - 4 y, y (0) = 3, y^{^{'}} (0) = - 63

y^{^{''''}} - 15 y^{^{''}} + 54 y = 0

\frac{d ^{2} y}{d x ^{2}} (1) + \frac{d y}{d x} (5) + 4 y = 0

What is the solution for 2y^{''}-13y^'+15y=0,y(0)=0,y^'(0)=17.5 ?
The solution for 2y^{''}-13y^'+15y=0,y(0)=0,y^'(0)=17.5 is y=5e^{5t}-5e^{(3t)/2}