What is the solution for 4y^{''}-4y^'+y=0,y(0)=1,y^'(0)=-1.5 ?

The solution for 4y^{''}-4y^'+y=0,y(0)=1,y^'(0)=-1.5 is y=e^{t/2}-2e^{t/2}t

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4y^{''}-4y^'+y=0,y(0)=1,y^'(0)=-1.5

4 y^{^{''}} - 4 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = - 1.5

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

Solution steps

4 y^{''} (t) - 4 y^{'} (t) + y = 0

Solve linear ODE:

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

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

What is the solution for 4y^{''}-4y^'+y=0,y(0)=1,y^'(0)=-1.5 ?
The solution for 4y^{''}-4y^'+y=0,y(0)=1,y^'(0)=-1.5 is y=e^{t/2}-2e^{t/2}t