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Popular >

4y^{''}-2y^'=7

Solution

4 y^{^{''}} - 2 y^{^{'}} = 7

Solution

y = c_{1} e^{\frac{t}{2}} + c_{2} - \frac{7 t}{2}

Solution steps

4 y^{''} (t) - 2 y^{'} (t) = 7

Solve linear ODE:

y = c_{1} e^{\frac{t}{2}} + c_{2} - \frac{7 t}{2}

y = c_{1} e^{\frac{t}{2}} + c_{2} - \frac{7 t}{2}

Popular Examples

y^{''}+4y^'+3y=3e^x+x

y^{^{''}} + 4 y^{^{'}} + 3 y = 3 e^{x} + x

x^{''}-3x^'-4x=8e^tcos(2t)

x^{^{''}} - 3 x^{^{'}} - 4 x = 8 e^{t} cos (2 t)

x^{''}-x=t,x^'(0)=0,x(0)=1

x^{^{''}} - x = t, x^{^{'}} (0) = 0, x (0) = 1

y^{'''}-3y^{''}-y^'+3y=e^{6x}

y^{^{'''}} - 3 y^{^{''}} - y^{^{'}} + 3 y = e^{6 x}

y^{''}-2y^'+y=t^{-1}e^t

y^{^{''}} - 2 y^{^{'}} + y = t^{- 1} e^{t}

Frequently Asked Questions (FAQ)

What is the solution for 4y^{''}-2y^'=7 ?
The solution for 4y^{''}-2y^'=7 is y=c_{1}e^{t/2}+c_{2}-(7t)/2