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Popular >

2y^{''}+y^'=2

Solution

2 y^{^{''}} + y^{^{'}} = 2

Solution

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

Solution steps

2 y^{''} (t) + y^{'} (t) = 2

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}-2y^'-15y=4

y^{^{''}} - 2 y^{^{'}} - 15 y = 4

y^{''}-3y^'-10y=54e^{7t}

y^{^{''}} - 3 y^{^{'}} - 10 y = 54 e^{7 t}

(d^2y)/(dx^2)+5(dy)/(dx)+6y=cos(4x)

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = cos (4 x)

2y^{'''}-5y^'+3y=3x^2e^{2x}

2 y^{^{'''}} - 5 y^{^{'}} + 3 y = 3 x^{2} e^{2 x}

y^{''}-6y^'+8y=-2e^{3x}

y^{^{''}} - 6 y^{^{'}} + 8 y = - 2 e^{3 x}

Frequently Asked Questions (FAQ)

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